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7. Alonzo and Mandy are selling raffle tickets at school for a fundraiser. Alonzo sells 5 tickets less than three times what Mandy sells. Together they sell a total of 43 tickets. Let n equal the number of tickets Mandy sells. Use an equation to determine the number of tickets Alonzo sells. Show how you arrived at your answer.​

a) The probability that more than 180 customers will take your free sample is approximately 0.9999.

b) The probability that fewer than 200 customers will take your free sample is approximately 0.0119.

c) Therefore, the probability that a customer will take a free sample and buy the product is 0.21.

d) The probability that between 60 and 80 customers will take the free sample and buy the product is approximately 0.043

a) Let X be the number of customers who take the free sample.

We know that X follows a binomial distribution with n = 327 and p = 0.58. To find the probability that more than 180 will take free sample, we need to find P(X > 180).

Using a binomial calculator or software, we get:

P(X > 180) = 1 - P(X ≤ 180) = 1 - binomial distribution (180, 327, 0.58, TRUE) ≈ 0.9999

Therefore, the probability that more than 180 customers will take your free sample is approximately 0.9999.

b) To find the probability that fewer than 200 will take your free sample, we need to find P(X < 200).

Using a binomial calculator or software, we get:.

P(X < 200) = binomial distribution (199, 327, 0.58, TRUE) ≈ 0.0119

Therefore, the probability that fewer than 200 customers will take your free sample is approximately 0.0119.

c) Let A be the event that a customer takes a free sample, and B be the event that the customer buys the product.

We are given P(B|A) = 0.35 and P(A) = 0.60.

Using the multiplication rule for dependent events, we get:

P(A ∩ B) = P(B|A) × P(A) = 0.35 × 0.60 = 0.21

Therefore, the probability that a customer will take a free sample and buy the product is 0.21.

d) Let Y be the number of customers who take the free sample and buy the product. We know that Y follows a binomial distribution with n = 327 and p = 0.21 (from part c). .

To find the probability that between 60 and 80 customers will take the free sample and buy the product, we need to find P(60 ≤ Y ≤ 80).

Using a binomial calculator or software, we get:

P(60 ≤ Y ≤ 80) = binomial distribution (80, 327, 0.21, TRUE) - binomial distribution (59, 327, 0.21, TRUE) ≈ 0.0434

Therefore, the probability that between 60 and 80 customers will take the free sample and buy the product is approximately 0.0434.

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Question: Do You Take The Free Samples Offered In Supermarkets? About 58 % Of All Customers Will Take Free Samples.

Furthermore, Of Those Who Take The Free Samples, About 37% Will Buy What They Have Sampled. Suppose You Set Up A Counter In A Supermarket Offering Free Samples Of A New Product. The Day You Were Offering Free Samples, 327Customers Passed By Your

Do you take the free samples offered in supermarkets? About 58% of all customers will take free samples. Furthermore, of those who take the free samples, about 37% will buy what they have sampled. Suppose you set up a counter in a supermarket offering free samples of a new product. The day you were offering free samples, 312 customers passed by your counter.(round your answers to four decimal places.)

a.) What is the probability that more than 180 will take your free sample?

b.) What is the probability that fewer than 200 will take your free sample?

c.) What is the probabilty that a customer will take a free sample and buy the product? Hint: Use the multiplication rule for dependent events. Notice that we are given the conditional probability P(buy|sample)=0.35, while P(sample)=0.60

d.) What is the probability that between 60 and 80 customers will take the free sample and buy the product? HInt: Use the probability of success calculated in part(c).

The value of the boxes, A , B and C are 22/4, 15/4 and 9 1/4 respectively

Note that from the information given, we have that the number in a box is the sum of the two numbers below it.

Then, we can deduce that;

A = The sum of the two mixed fractions, 3 1/4 and 2 1/4

B = The sum of the two mixed fractions, 2 1/4 and 1 1/2

Now, add the values

A = 3 1/4 + 2 1/4

convert to improper fractions

A = 13/4 + 9/4

Add the values

A = 22/4

B = 2 1/4 + 1 1/2

convert to improper fractions

B = 9/4 + 3/2

B =9 + 6 /4

B = 15/4

Then , the value of C = A + B

C = 22/4 + 15/4

C = 37/4

C = 9 1/4

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The correct equation for the hanger balance is:= w = 2

How to balance equations?

The hanger balance equation is typically used in physics experiments to determine the weight of an object by comparing it to known weights on the other side of a balance. The equation is based on the principle of equilibrium, which states that the sum of the forces acting on an object must be zero for it to remain stationary.

The correct equation for the hanger balance is:

w = 2

This equation simply states that the weight of the object being measured (represented by "w") is equal to a known weight of 2 units. This indicates that the object being measured has a weight of 2 units.

The other equations provided, such as "6 = w + 2" and "6 = w - 2", do not accurately represent the hanger balance equation because they do not take into account the known weight on the other side of the balance. In order to determine the weight of an object using a hanger balance, it is necessary to have a known weight on the other side of the balance to compare it to.

In summary, the correct equation for the hanger balance is w = 2, which represents the weight of the object being measured as 2 units.

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Answer: they are adding 30 each time

Step-by-step explanation:

in 320 to 350, it adds 30 because 20 plus 30 equals 50 then you can add 300 which is 350 then 350 plus 30 is 380 which is also the next number which means you are adding 30 each time and for the first box you subtract 30 from 350 which is 320 and for the last box you add 30 which is 380 + 30 which is 410 so that is your answer.

Answer:

To solve the equation |x+3|=9, we need to split it into two separate equations, one for the positive value and one for the negative value of the absolute value:

For the positive value:

x+3=9

Solving for x, we get x=6

For the negative value:

-(x+3)=9

Multiplying both sides by -1, we get:

x+3=-9

Solving for x, we get x=-12

Therefore, the solutions to the equation |x+3|=9 are x=6 and x=-12.

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For the the inequality –3(2x – 5) < 5(2 – x) the correct options are: x < 5, –6x + 15 < 10 – 5x

What is inequalities?

In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal. It is a statement that compares two values, usually using one of the following symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).

The correct representations of the inequality –3(2x – 5) < 5(2 – x) are:

x < 5 (obtained by simplifying the inequality and solving for x)

–6x + 15 < 10 – 5x (obtained by distributing the terms and simplifying the inequality)

Therefore, the correct options are:

x < 5

–6x + 15 < 10 – 5x

The options that describe number lines are not applicable to this inequality since they represent a single value, whereas an inequality represents a range of values that satisfy the inequality.

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a) The area of the square  for side length [tex]3[/tex] is [tex]9[/tex][tex]cm^{2}[/tex].

The area of the square for side length [tex]100[/tex] is [tex]10000[/tex][tex]cm^{2}[/tex]

The area of the square for side length  [tex]25[/tex] is [tex]625cm^{2}[/tex].

The area of the square  for the side length [tex]s[/tex] is   [tex]s^{2}cm^{2}[/tex].

b) No the side length of the square and area are not directly proportional.

The area of a square is the amount of space enclosed within the square, and it can be calculated using the formula A = [tex]s^{2}[/tex], where A is the area and s is the length of one side of the square.

According to the given information

The area of a square is the amount of space enclosed within the square, and it can be calculated using the formula A =[tex]s^{2}[/tex]

[tex]A = s^{2} = 3^{2} = 9cm^{2}[/tex]

[tex]A = s^{2} = 10^{2} = 10000cm^{2}[/tex]

[tex]A = s^{2} = 25^{2} = 625cm^{2}[/tex]

[tex]A = s^{2} = s^{2} = s^{2} cm^{2}[/tex]

Therefore area of the square are [tex]9cm^{2} ,10000cm^{2}, 625cm^{2} ,s^{2}cm^{2}[/tex]

Therefore the side length of the square and area are not directly proportional they are proportional to the square root of area.

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A scatter plot would be more appropriate to construct for the data, given the context of the problem. The reason is that the marine biologist is interested in seeing the relationship between a manatee's weight and food consumption.

A scatter plot is a type of graph that displays the relationship between two variables, where each variable is plotted along one axis, and a point is placed at the intersection of the two values. In this case, weight would be plotted along one axis and food consumption along the other axis.

A scatter plot allows the researcher to see if there is a relationship between the two variables, and if so, what type of relationship it is (positive, negative, or no correlation). Therefore, a scatter plot is the most appropriate way to display the relationship between a manatee's weight and food consumption.

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The function g(-7) * f(-7) is approximately equal to *-8056.5*.

What is a function?

A function is a mathematical rule that assigns a unique output value to each input value from a given set. It represents a relationship between two sets of numbers in which each input has exactly one output. A function can be expressed symbolically, graphically, or verbally and is used to model real-world phenomena, solve equations, and make predictions in various fields of study.

According to the given information

To find g(-7) and f(-7), we need to substitute -7 for y in the function g(y) = -2ᵇ - 4b + 13 and x in the function f(x) = -2x² - 4x + 13.

g(-7) = -2⁻⁷ - 4⁻⁷ + 13

Simplifying this expression gives:

g(-7) = -1/128 + 28 + 13

g(-7) = 141 - 1/128

Therefore, g(-7) is approximately equal to 140.9922 .

f(-7) = -2(-7)² - 4(-7) + 13

Simplifying this expression gives:

f(-7) = -98 + 28 + 13

f(-7) = -57

Therefore, f(-7) is equal to -57.

So, g(-7) * f(-7) is approximately equal to -8056.5.

The correct question is

g(y ) = − 2ᵇ − 4b + 13 and f(x)=−2x² −4x+13, find g( − 7 ) f(−7)

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Answer:

True

Step-by-step explanation:

Since C has to add up to 180 and we already have 150 we can assume that that other angle is 30. The sum of angles in a triangle always has to equal 180. 120+30=150 meaning B also equals 30. B+A=150 therefore making it true.

Answer: r = 45°

Step-by-step explanation:

All triangles angles add up to 180 degrees.

With that said we can use the given information and create an equation to solve.

55° + 80° + r = 180°

Lets solve for r.

55° + 80° + r = 180°

first lets combine like terms.

135° + r = 180°

now lets subtract 143° from both sides

135° + r = 180°

-135°       -135°

r = 45°

The length of the pole is approximately 412.7 feet.

What is the tangent function?

The tangent function is a mathematical function that relates the ratio of the length of the side opposite to an acute angle in a right triangle to the length of the adjacent side. It is defined as the ratio of the sine of the angle to the cosine of the angle.

We can solve this problem using trigonometry. Let's call the length of the pole "x". We can then use the tangent function to relate the angle that the pole makes with the vertical to the length of the shadow cast by the pole.

The tangent of the angle between the pole and the vertical is equal to the opposite side (length of the shadow) divided by the adjacent side (length of the pole).

tan(7°) = opposite / adjacent

tan(7°) = 49 / x

We can solve for x by multiplying both sides by x and then dividing both sides by tan(7°):

x = 49 / tan(7°)

Now we know the length of the pole is:

x = 49 / tan(7°) = 412.7 ft (rounded to one decimal place)

Therefore, the length of the pole is approximately 412.7 feet.

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The correct answer is: No, because for each input there is not exactly one output.

In mathematics, a function is a relation between two sets, where each element in the first set (called the domain) is associated with exactly one element in the second set (called the codomain or range). A function assigns a unique output value (dependent variable) to each input value (independent variable) from the domain.

The given relation does not represent a function because for some inputs there are multiple outputs, violating the "one-to-one" or "vertical line test" rule.

The correct answer is: No, because for each input there is not exactly one output.

In this relation, we can see that x = 1 has two different outputs, y = 5 and y = -1/2. Therefore, the relation does not meet the criteria of a function as it violates the requirement of having exactly one output for each input.

Therefore, The correct answer is: No, because for each input there is not exactly one output.

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Answer:

$30

Step-by-step explanation:

6x3=18

        +

4x3=12

=30

After answering the presented question, we can conclude that As a equation result, Emily's automobile will be valued roughly $19,105.25 after 8 years.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "[tex]2x + 3 = 9[/tex]" asserts that the phrase "[tex]2x + 3[/tex]" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "[tex]x2 + 2x - 3 = 0[/tex]." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

Emily's car will be worth 100% - 18% = 82% of its original value after one year, or 0.82 times its initial value.

After two years, the car is worth 0.82 times its initial value, or 0.822% of its original value.

Similarly, the car will be worth 0.828% of its initial value after 8 years.

Hence, after 8 years, Emily's automobile will be worth:

In 8 years, the value is $55,000 x 0.82.

After 8 years, the value is $19,105.25. (rounded to the nearest cent)

As a result, Emily's automobile will be valued roughly $19,105.25 after 8 years.

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Answer:

None of them, 3x + 15 is correct.

Step-by-step explanation:

In order to apply the distributive properly correctively, we need to multiply everything in the parentheses. For an example, lets look at the given expression:

[tex]3(x+5)[/tex]

We multiply everything in the parentheses by 3

[tex]3x+15[/tex]

Looking at out choices, none of them uses the distributive property correctly.

Answer:

P=40 and y was decreased by 40%

Step-by-step explanation:

Let's set up an equation as follows. In this case, we will set y will be equivalent to 1, as the number can be any value for this equation in the other fraction as the original number. Let us then represent the new number, 0.6y, or 0.6*1 which will be equivalent to 0.6 itself, and we will set that equal to 100-p as p will be the amount of percent it was decreased by. Here is the equation as follows:

We can use a method of solving fractions that is known as the Cross-multiplication property, which demonstrated in the image attached below this answer. Using this property, we can determine and simplify the equation to as follows:

[tex]1*(100-p)=0.6(100)[/tex], which can be simplified to [tex]100-p=60[/tex], and then solving the equation gives us the answer:

[tex]p=40[/tex]

P=40

The rate at which water is being pumped into the tank is 11,760 cm3/min.

          V = (1/3)πr2h

          Using similar triangles:

          (r / 2) = (2 / 6)

          r = 2/3 * 4r = 8/3 cm

          dV / dt = (πr2 / 3)dh / dt

         dV / dt = pump rate - leak rate

      = pump rate - 10,500 cm3/mindh / dt

      = 20 cm/minr = 8/3 cm

        pump rate - 10,500 = (π(8/3)2 / 3) * 20pump rate - 10,500

     = 2114.67pump rate

     = 11,760 cm3/min

Therefore, the rate at which water is being pumped into the tank is 11,760 cm3/min.

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The output of the function g(x) = [tex]3^{(\frac{x}{2} )}[/tex] when x = 2 is 3.

g(x) is a function as defined as follows:

g(x) = [tex]3^{(\frac{x}{2} )}[/tex]

If we input n2 into the g(x), the output g(x) can be gotten as follows:

Therefore,

g(x) = [tex]3^{(\frac{x}{2} )}[/tex]

where

x = 2

Therefore,

[tex]3^{(\frac{2}{2} )}[/tex] = 3¹

Therefore,

the output is 3.

g(2) = 3

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She could solve for (x+3)² and find two solutions, x = (-3 + √(33/2)) / 2 and x = (-3 - √(33/2)) / 2.

it's a second-degree quadratic equation which is an algebraic equation in x. Ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form.

The three steps that Inga could use to solve the quadratic equation 2x² + 12x – 3 = 0 are:

1. Use the quadratic formula: Inga could use the quadratic formula x = (-b ± √(b² - 4ac)) / 2a, where a = 2, b = 12, and c = -3.

2. Factor the quadratic expression: Inga could factor the quadratic expression into (2x - 1)(x + 3) = 0 and then use the zero product property to find the solutions x = 1/2 and x = -3.

3. Complete the square: Inga could use the method of completing the square by adding and subtracting (6/2)² = 9 to the left side of the equation, giving 2(x+3)² - 33 = 0. Then she could solve for (x+3)² and find two solutions, x = (-3 + √(33/2)) / 2 and x = (-3 - √(33/2)) / 2.

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Answer:

Step-by-step explanation:

f=133

a=93

c=140

According to the infographic, women constitute approximately 15-19% of members of Congress, less than 15% of state legislators, and 25-50% of statewide executives and mayors in the top 100 cities.

According to the information provided in the infographic, the following options apply:

Women constitute approximately 25-50% of statewide executives and mayors in the top 100 cities.

Women constitute approximately 15-19% of members of Congress.

Women constitute less than 15% of state legislators.

Therefore, the correct options are:

15-19%

Less than 15%

25-50%

The infographic presents data on the percentage of women overall in elected office and the share of Latinas in elected office. The data indicates that women constitute less than 15% of state legislators, approximately 15-19% of members of Congress, and 25-50% of statewide executives and mayors in the top 100 cities. This suggests that women are underrepresented in elected office at all levels of government, with the exception of statewide executives and mayors in the top 100 cities. The infographic underscores the need for greater gender diversity in elected office, and the importance of supporting and encouraging women to run for political office at all levels of government.

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Complete question:

The infographic shows percentages of women overall in elected office as well as the share of Latinas in elected office. Women constitute approximately what percentage of members of Congress, statewide executives, state legislators, and mayors in the top 100 cities? Check all that apply.

19-25%

Less than 15%

15-19%

25-50%

When a confounding variable is present in an experiment, one cannot tell whether the results were due to the independent variable or the dependent variable. The correct option is a) independent variable or the dependent variable.

A confounding variable is any variable that influences the dependent variable or response variable and is also

correlated with the independent variable. Because it is difficult to determine which variable is causing changes in the

dependent variable, it is also known as a confounding variable.

In other words, a confounding variable is a variable that can affect the dependent variable in an experiment, making it

impossible to determine the relationship between the independent variable and the dependent variable.

Therefore, when a confounding variable is present in an experiment, one cannot tell whether the results were due to

the independent variable or the dependent variable.

Consequently, researchers must take steps to identify and eliminate or control the effect of confounding variables to obtain valid and reliable results.

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If the sample size is large and the probability of success is not too close to 0 or 1, using the normal distribution to approximate the binomial probability will generally give a more accurate answer than using the binomial tables. However, if the sample size is small or the probability of success is very close to 0 or 1, using the binomial tables may be more accurate.

If the sample size is large (typically, n ≥ 30) and suppose that the probability of success (p) is not too close to 0 or 1, then we can use the normal distribution. As it gives more approximate value to the binomial probability which will generally give a more accurate answer than using the binomial tables.

This is because the normal distribution provides a more precise approximation of the binomial distribution as the sample size increases.

However, if the the probability of success is very close to 0 or 1 or sample size is small then using the binomial tables to calculate the probability directly may be more accurate. In general, it's important to check the conditions for using the normal approximation before using it and to use good judgment in deciding which method is more appropriate for a given problem.

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10 to the 9th power is 10 times 10 to the 8th power.

To graph g(x), we must replace x with x + 1 in the function f(x) = 2x - 5: g(x) = f(x + 1) = 2(x + 1) - 5 = 2x - 3 (a) To display the g of x line that passes through the coordinates 0, -4, and 2, 0, we replace x = 0 and x = 2 in the equation g(x) = 2x - 3:

g(0) = 2(0) - 3 = -3

g(2) = 2(2) - 3 = 1

Hence the line's points are (0, -3) and (2, 1):

yaml Copy code | 5 |- * (2,1) | 4 |- | 3 |- * (0,-3) | 2 |- | 1 |- | 0 |—————————— 0 1 2 3 4 5\s(b) (b) To display the g of x line that passes through points 0, -3, 4, 5, we replace x = 0 and x = 4 in the equation g(x) = 2x. - 3:

g(0) = 2(0) - 3 = -3

g(4) = 2(4) - 3 = 5

Hence the line's points are (0, -3) and (4, 5):

Copy code in yaml | 5 |- * (4,5)

|\s4 |-\s |\s3 |- * (0,-3)\s |\s2 |-\s |\s1 |-\s |\s0 |

————————-\s 0 1 2 3 4 5\s(c) (c) To display the line labeled g of x that goes through points -5, -3, and 0, 7, we use the equation g(x) = 2x - 3:

g(-5) = 2(-5) (-5) - 3 = -13\sg(0) = 2(0) - 3 = -3

Thus the line points are (-5, -13) and (0, -3):

| 5 |- | 4 |- | 3 |- | 2 |- | 1 |- | 0 |- * (0,-3) | -1 |- (-5,-13)

\ \s ——————-\s -5 -4 -3 -2 -1 0\s(d) To draw the g of x line that passes between points 0, -7, and 5, 3, In the equation g(x) = 2x - 3 we substitute x = 0 and x = 5:

g(0) = 2(0) - 3 = -3

g(5) = 2(5) (5) - 3 = 7

Hence the line's points are (0, -3) and (5, 7):

| 7 |- * yaml Copy code (5,7)

|\s6 |-\s |\s5 |- \s | * (0,-3) (0,-3)

4 |-\s |\s3 |-\s |\s2 |-\s |\s1 |-\s |\s0 |

————————-\s 0 1 2 3 4 5.

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Step-by-step explanation:

Area of a triangle = 1/2 * base * height

 For this triangle   base =  9 m   height =  8 m

1/2 ( 9 ) ( 8) = 36 m^2

The cosine of angle X is 0.75 of triangle WXV.

In a right-angled triangle, the cosine of an angle is equal to the adjacent side divided by the hypotenuse. Therefore, to find cos(X) in triangle XWV, we need to find the adjacent and hypotenuse sides that correspond to angle X.

We know that WV = 72, which is the length of the side opposite the right angle. To find the length of the hypotenuse XV, we can use the Pythagorean theorem: [tex]XV^{2}[/tex] = [tex]WV^{2}[/tex] + [tex]WX^{2}[/tex], where WX is the length of the side adjacent to angle X.

Solving for WX, we get:

[tex]WX^{2}[/tex] = [tex]XV^{2}[/tex] - [tex]WV^{2}[/tex]

[tex]WX^{2}[/tex]= [tex]90^{2}[/tex] - [tex]72^{2}[/tex]

[tex]WX^{2}[/tex] = 2916

WX = 54

Now we can find cos(X):

cos(X) = adjacent/hypotenuse

cos(X) = WX/WV

cos(X) = 54/72

cos(X) = 0.75

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The experimental probabilities have their values to be P(3) = 1/12, P(6) = 1/4 and P(Less than 4) = 1/2

Experimental probability of 3

From the table of values, we have

n(3) = 1

Total = 12

So, we have

P(3) = 1/12

Experimental probability of 6

From the table of values, we have

n(6) = 3

Total = 12

So, we have

P(6) = 3/12

P(6) = 1/4

Experimental probability of less than 4

From the table of values, we have

n(Less than 4) = 6

Total = 12

So, we have

P(Less than 4) = 6/12

P(Less than 4) = 1/2

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