If a fair coin is tossed 6 times, what is the probability, rounded to the nearest thousandth, of getting at most 2 heads?
Answers
Answer:
[tex] \displaystyle 0.344[/tex]
Step-by-step explanation:
we are given that a coin is tossed 6 times and we want to find the probability of getting at most 2 heads.
To solve this problem,we can consider binomial distribution, which is given by
[tex] \displaystyle P(X = r) = \binom{n}{r} {p}^{r} {q}^{n - r} [/tex]
where:
P = binomial probabilityr = number of times for a specific outcome within n trials[tex]{n \choose r}[/tex] = number of combinationsp = probability of success on a single trialq = probability of failure on a single trialn = number of trialswe want to figure out the probability of getting at most 2 heads out of 6 trials , The probability can therefore be found by adding up all the binomial distributions including X=2 and less than it, Thus
[tex] \displaystyle P(X \leq 2) = P(X=0)+P(X=1)+P(X=2) [/tex]
[tex] \displaystyle P(X \leq 2) = \binom{6}{0} {p}^{0} {q}^{6 - 0} + \binom{6}{1} {p}^{1} {q}^{6- 1} + \binom{6}{2} {p}^{2} {q}^{6 - 2} [/tex]
when a coin is tossed, the probability of getting both head (success) and tail (failure) are ½ which is why ,the variables, p and q are assigned to ½. therefore substitute
[tex] \rm\displaystyle P(X \leq 2) = \binom{6}{0} { \left( \frac{1}{2} \right) }^{0} { \bigg( \frac{1}{2} \bigg) }^{ 6- 0} + \binom{6}{1} { \bigg( \frac{1}{2} \bigg) }^{1} { \bigg( \frac{1}{2} \bigg) }^{6 - 1} + \binom{6}{2} { \bigg( \frac{1}{2} \bigg)}^{2} { \bigg( \frac{1}{2} \bigg) }^{6- 2} [/tex]
since p and q are the same. it won't make any difference to write all the product of p and q as (½)⁶:
[tex]\rm\displaystyle P(X \leq 2) = \binom{6}{0} { \bigg( \frac{1}{2} \bigg) }^{ 6} + \binom{6}{1} { \bigg( \frac{1}{2} \bigg) }^{6} + \binom{6}{2} { \bigg( \frac{1}{2} \bigg) }^{6}[/tex]
In the expression the term (½)⁶ is common thus factor it out:
[tex]\rm\displaystyle P(X \leq 2) = { \bigg(\frac{1}{2}\bigg) }^{ 6} \left( \binom{6}{0} + \binom{6}{1} + \binom{6}{2} \right) [/tex]
calculate the combinations:
[tex]\rm\displaystyle P(X \leq 2) = { \bigg(\frac{1}{2}\bigg) }^{ 6} \left(1+6+15\right) [/tex]
simplify addition:
[tex]\rm\displaystyle P(X \leq 2) = { \bigg(\frac{1}{2}\bigg) }^{ 6} \left(22\right) [/tex]
simplify exponent:
[tex]\rm\displaystyle P(X \leq 2) = { \bigg(\frac{1}{64}\bigg) } \left(22\right) [/tex]
simplify multiplication:
[tex]\rm\displaystyle P(X \leq 2) = \frac{22}{64} [/tex]
dividing yields:
[tex]\rm\displaystyle P(X \leq 2) = 0.34375 [/tex]
[tex]\rm\displaystyle P(X \leq 2) \approx 0.344 [/tex]
In conclusion
The answer is 0.344
Related Questions
graph the function. f(x)=−∣∣x+2∣∣+1
Answers
Answer:
f(x)=-|x+2|+1
I've attached the graph for it
Explanation:I done the assessment
Use the distributive property to write an equivalent expression.
8(3v+3w-2)
Answers
I multiplied all the numbers inside the parenthesis to 8, so (8 x 3w),(8 x 3v),(8 x -2). Basically Distrbutive property is you distribute the 8 into the numbers inside the parenthesis and by distribute you just multiply. Lemme know if this is the answer you were looking for!
Answer:
8(3v+3w-2)=(8×3v+8×3w-8×2)
Step-by-step explanation:
8×3v=24v.
8×3w=24w. [24v+24w-16]=(8×3v+8×3w-2×8)
8×(-2)=-16.
does anyone have the answers for all?
Answers
Answer and Step-by-step explanation:
1-6
a.
What you can do is plug in 6 and start by doing the first machine first, then the second. If this doesn't work, do the second machine, then the first machine.
The order that works is second machine, then first machine.
Second Machine:
y = [tex](6)^{2} -6[/tex] = 36 - 6 = 30
Plug into first machine now.
First Machine:
y = [tex]\sqrt{(30) - 5} = \sqrt{25} = 5[/tex]
We see that the result is 5.
b. If we were to do the order of second machine, then first machine, we will never get a negative result (or -5 for that matter), due to the fact that you can't algebraically square root a negative number.
However, if we were to do the order of first machine, second machine, we can get a negative number. To get -5, we plug in 6 for x in the first machine, getting an answer of 1. We plug this into the second machine, getting 1^2 - 6, which results in -5.
1-7. The absolute value of a value is the positive version of that value.
a. |54| = 54
b. [tex]-|-7\frac{3}{5}|[/tex] = [tex]-7\frac{3}{5}[/tex]
c. |3| - |-1| = 3 - 1 = 2
d. |2.2 - 5.13| = |-2.93| = 2.93
1-8.
a.
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(5 boxes on each side)
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(6 boxes on each side)
b. The amount of squares on each side of the figure increases by 1.
c. There would be 1 square, because we know that the pattern is there is 2 squares added to the next figure, 1 at each end. If we go back a figure, we take away 2 squares.
1-9.
a. -42 - 17 = -59
b. 8 - (-9) = 8 + 9 = 17
c. 8(-9) = -72
d. -42 ÷ (-7) = 6
e. -2(-3)(-4) = 6(-4) = 24
f. -18 - 7 = -25
g. [tex](-5)^{2}[/tex] = 25
h. [tex]-5^{2} = -(5)^2 = -(25)[/tex] = -25
i. [tex]\sqrt{49}[/tex] = 7
1-10. x = 2 Plug 2 in for x, then solve.
a. y = 7 - 3(2) = 7 - 6 = 1
b. y = [tex](2)^2 -1[/tex] = 4 - 1 = 3
c. y = [tex]\frac{18}{2}[/tex] = 9
#teamtrees #PAW (Plant And Water)
I hope this helps!
Rick had 6 meters 63 centimeters of wire in his toolshed. He bought 2 meters 24 centimeters more wire and put this in his shed. The next day, he used 344 centimeters of wire. How much wire does Rick have left in the toolshed?
Answers
Answer:
543 centimeters or 5 meters 43 centimeters
Step-by-step explanation:
663+224=887
887-344=543
Visualize 4.385 on a number line using magnification.
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Answer:
Um srry I am a hack I like this app Haha I hadked this girls brainy hehehe
Find the Product.
1.45 X 3.8-
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Answer:
the answer for this question is 5.51
Which is the graph of f(x) = 1/4 (4)^x ?
Answers
Answer:
The only graph that is fully shown.
Step-by-step explanation:
I did the math and the points check out.
What is the smallest whole number that is above square root of 17
Answers
Answer:
5
Step-by-step explanation:
√17 = 4.124105626
smallest would be 5 since it is already above 4
∴the smallest whole number that is above √17 is 5
Hope my answer helped u :)
Which of the following fractions has the greatest value?
3/4
5/8
5/6
5/9
3/7
Answers
We can see that 420/504 is the largest value among the fractions. the fraction 5/6 has the greatest value.
To determine which fraction has the greatest value, we can compare the fractions by finding a common denominator and comparing the numerators.
Let's find a common denominator for all the fractions, which is the least common multiple (LCM) of the denominators.
The denominators are 4, 8, 6, 9, and 7.
The LCM of 4, 8, 6, 9, and 7 is 504.
Now, let's convert each fraction to have a denominator of 504:
3/4 = (3/4) * (126/126) = 378/504
5/8 = (5/8) * (63/63) = 315/504
5/6 = (5/6) * (84/84) = 420/504
5/9 = (5/9) * (56/56) = 280/504
3/7 = (3/7) * (72/72) = 216/504
Comparing the numerators, we can see that 420/504 is the largest value among the fractions.
Therefore, the fraction 5/6 has the greatest value.
for more such question on fractions visit
https://brainly.com/question/78672
#SPJ8
help help help......
Answers
========================================================
Explanation:
Point C is located at (-6,3). The x coordinate is x = -6.
Going from x = -6 to x = -1 is 5 units to the right. We move another 5 units to the right to go from x = -1 to x = 4 when arriving at its reflected location (4,3). The y coordinate stays the same the entire time.
It might help to refer to the diagram below.
How do you translate "A number, x, multipled by one thousand. " as a variable expression
Answers
U have ur x variable and it’s being multiplied by 1000
So it’s just 1000•x or 1000x
I hope this helps :)
PLEASE HELP YOU GET BRAINLY I HAVE A LIMITED TIMEE
Answers
Answer:
2a
b+b+b+b+b
C^3
d*d*d*d
I only know the first 4
I hope this helps
Step-by-step explanation:
Answer:
Step-by-step explanation:
e. x
∑ e
1
- or more simply, xe.
f. f^y
Solve for x: 1/3(21-3x)=1/2(8-4x)
Answers
Answer:
x = -3
Step-by-step explanation:
[tex] \frac{1}{3} -(21 - 3x) = \frac{1}{2} (8 - 4x)[/tex]
[tex]21 - 3x = 3(4 - 2x)[/tex]
[tex]21 - 3 x = 12 - 6x[/tex]
[tex] - 3x + 6x = 12 - 21[/tex]
[tex]3x = - 9[/tex]
[tex]x = - 3[/tex]
A man mixes 90 litres of milk, containing 10% of water with 60 liters of milk containing 20% of water, then the percent of water in the minture is?
Answers
Answer:
it is 15 percent than
Step-by-step explanation:
hope i could help
a mans age today is four years less than five times the age of his oldest son. let a represent the son's age. write an expression to represent the man's age.
Answers
Answer:
m = 5s - 4
Step-by-step explanation:
Man = m
Son = s
the mans age is 4 years less than 5 times his sons age
5 times his sons age is 5s
4 less than that is 5s - 4
The man's age is 5s - 4 or m = 5s - 4
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Plz help me answer this question
Answers
Answer:
I think it's the top left one
Step-by-step explanation:
The length is 6, the width is 3, and the height is 4, which matches the expression.
Step-by-step explanation:
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Answers
Answer:
it can`t be solved unless you have an integer in place of F and B
otherwise this can`t be solved
Answer:
d=b(f+3)
Step-by-step explanation:
fb+3b=d
Swap sides so that all variable terms are on the left hand side.
d=fb+3b
hope it helps :)
A new cars salesperson, sold an average of $59,699 per day for the first 4 days she worked. The next 11 days she worked, she sold an average of $49,221. How much did she sell on average per day over the entire time she worked??
Answers
Answer:
5,000
Step-by-step explanation:
Solve using a weighted average like so:
{ (6 days)($34,000) + (4 days)($45,000) }/(6 days + 4 days) = $38,400
It doesn't appear as if the correct answer is listed in the choices? You can tell from the information given that the answer must be between $34,000 & $45,000!
The regular price of a pair of
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Answers
Answer:
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Step-by-step explanation:
0 less than or equal to theta less than 2pi
sin theta= 1/2
HELP QUICK PLEASE !!!
WILL GIVE BRAINLIEST !
Answers
Answer:
theta = 4.5642792103077898247
Step-by-step explanation:
0 <= theta < 2Pi sin(theta) = 1/2
so
2Pi sin(theta) = 1/2
Pi sin(theta) = 1/4
sin(theta) = 1/(4Pi)
sin(theta) = .0795774715459
theta = arcsin(.0795774715459) = 4.5642792103077898247
Which linear inequality is represented by the graph?
Oys-x-1
O yzx-1
O y<3x-1
Oy> 3x - 1
Answers
Answer:
The fourth answer choice is correct.
y>3x-1
The linear inequality that is represented here is y> 3x - 1. The last option is correct.
What is a linear inequality?These are inequalities that shows linear functions. It is showing the data that is not equal in the graph that is presented.
We can see that the line cuts through 3 at the X axis and -1 at the y axis.
Read more on linear inequalities here:
https://brainly.com/question/17152894?referrer=searchResults
f(x) = x² + 3x – 4 if x = 5a
Answers
Answer:
Step-by-step explanation:
f(5a) = ([tex]5a)^{2}[/tex] + 3× 5a - 4
The diameter of a circle is 21 inches. Find the area of the circle. (Use 22/7 as the approximation of pi.)
Answers
Step-by-step explanation:
Area of a circle is pi times r-square
[tex]\pi \: {r}^{2} [/tex]
So...
[tex] \frac{22}{7} \times \frac{21}{2} \times \frac{21}{2} = \frac{22 \times {21}^{2} }{28} [/tex]
Do the rest yourself, my calculator and pen are not handy. Sorry
3 Factorise 5y - 6py
Answers
Step-by-step explanation:
5y-6py
y(5-6p)
Answer
hope it helps
Answer:
5y - 6py
y(5-6p)
is the answer
Giải phương trình x^4-2x^3+2x^2-x-6=0
Answers
Answer:
[tex]x_{1} = - 1. \: \: x_{2} = 2[/tex]
Step-by-step explanation:
attached
Find the Value of X
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Answers
10/6=(2x+1)/(x+1)
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10x+10=12x+6
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How does the graph of g(x) = (x + 5)3 - 9 compare to the parent function f(x) = x3?
g(x) is shifted 5 units to the left and 9 units down.
g(x) is shifted 9 units to the left and 5 units down.
g(x) is shifted 5 units to the right and 9 units down.
g(x) is shifted 9 units to the left and 5 units up.
Answers
a
Step-by-step explanation:
five to left and 9 to down
Hopefully that helps youuu!!
You start at (-4, -5). You move up 5 units. Where do you end?
Answers
Answer:
-4,0
Step-by-step explanation:
Moving up 5 units means moving 5 positive units in the y axis.
-5 + 5 = 0.
Therefore, you end up in (-4,0)
what is the probability of reaching into the bag and picking a red marble and then drawing again (without replacing the marble you picked the first time) and picking a red marble. Please help. i have acellus btw
Answers
Answer:
To solve you would need the exact number of all colored marbles
Why is speed not important in math ?
Answers
Since everything in math is interconnected, the deeper your understanding of the foundational topics you learn, the more easily you’ll understand new concepts that build upon the foundations.
As a concept, speed or rates of change are a key topic in Calculus. So speed is also important that way too.