16. A section of an exam contains four True-False questions. A completed exam paper is selected at random, and the four answers are recorded. a. List all outcomes in the sample space. b. Assuming the outcomes to be equally likely, find the probability that all the answers are the same. c. Assuming the outcomes to be equally likely, find the probability that exactly one of the four answers is "True." d. Assuming the outcomes to be equally likely, find the probability that at most one of the four answers is "True."

Answers

Answer 1

Answer:

a

[ FFFF] , [FFFT] , [FFTF] , [FFTT]

[FTFF] , [FTFT] , [FTTF], [FTTT]

[TFFF] , [TFFT] , [TFTF] , [TFTT]

[TTFF] , [TTFT],[TTTF] , [TTTT]

b

  [tex]P(A) =  \frac{1}{8}[/tex]

c

 [tex]P(B) = \frac{1}{4}[/tex]

d

[tex]P(C) = \frac{5}{16}[/tex]

Step-by-step explanation:

From the question we are told that

The number of True - False question is n = 4

The number of answers recorded are k = 4

Generally the outcomes in the sample space are 16 and they are listed below

[ FFFF] , [FFFT] , [FFTF] , [FFTT]

[FTFF] , [FTFT] , [FTTF], [FTTT]

[TFFF] , [TFFT] , [TFTF] , [TFTT]

[TTFF] , [TTFT],[TTTF] , [TTTT]

Generally from the list of the possible outcome we see that the number of outcome where the answers are the same is 2 i.e [TTTT] and [FFFF]

So the probability that all the answers are the same is mathematically represented as

[tex]P(A) = \frac{2}{16}[/tex]

=> [tex]P(A) = \frac{1}{8}[/tex]

Generally from the list of the possible outcome we see that the number of outcome where exactly one answer is true is 4 i.e [FFTF] , [FFFT],[TFFF] , [FTFF]

So the probability that exactly one of the four answers is "True." is mathematically represented as

[tex]P(B) = \frac{4}{16}[/tex]

=> [tex]P(B) = \frac{1}{4}[/tex]

Generally from the list of the possible outcome we see that the number of outcome where at most one of the four answers is true is 5 i.e [FTFF] , [FFFF] , [FFTF] , [FFFT] ,[TFFF]

So the probability that at most one of the four answers is mathematically represented as

[tex]P(C) = \frac{5}{16}[/tex]

Answer 2

The probabilities of all same, exactly one true, and most one of the four are true is 0.125, 0.25, and 0.3125 respectively.

What is probability?

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

A section of an exam contains four True-False questions.

A completed exam paper is selected at random, and the four answers are recorded.

Total event = 16

A.  The sample space will be shown in the table below.

[tex]\rm Sample \ space = 16 \ \begin{Bmatrix}FFFF & FFFT & FFTF & FFTT \\FTFF & FTFT & FTTF & FTTT \\TFFF & TFFT & TFTF & TFTT \\TTFF & TTFT & TTTF & TTTT\end{Bmatrix}[/tex]

B.  The probability that all the answers are the same will be.

Favorable event = 2 ={(TTTT, FFFF}

Then we have the probability,

[tex]\rm P(B) =\dfrac{2}{16} =\dfrac{1}{8} = 0.125[/tex]

C.  The probability that exactly one of the four answers is "True".

Favorable event = 4 {(FFFT, FFTF, FTFF, TFFF}

Then we have the probability,

[tex]\rm P(C) =\dfrac{4}{16} =\dfrac{1}{4} = 0.25[/tex]

D.  The probability that at most one of the four answers is "True".

Favorable event = 5 {(FFFF, FFFT, FFTF, FTFF, TFFF}

Then we have the probability,

[tex]\rm P(D) =\dfrac{5}{16} =0.3125[/tex]

More about the probability link is given below.

https://brainly.com/question/795909


Related Questions

prove cosec 2x + cot 2x = cot x​

Answers

csc(2x) + cot(2x) = 1 / sin(2x) + cos(2x) / sin(2x)

csc(2x) + cot(2x) = (1 + cos(2x)) / sin(2x)

csc(2x) + cot(2x) = (1 + cos(2x)) / (2 sin(x) cos(x))

csc(2x) + cot(2x) = cos²(x) / (sin(x) cos(x))

csc(2x) + cot(2x) = cos(x) / sin(x)

csc(2x) + cot(2x) = cot(x)

what is the slope.of the line passing points (1, -5) and (4, 1)

Answers

Answer:

[tex]\huge{\boxed{\sf{ 2 }}}[/tex]

Step-by-step explanation:

Let the points be A and B

A ( 1 , -5 ) [tex]\longrightarrow[/tex] ( x1 , y1 )

B ( 4 , 1 ) [tex]\longrightarrow[/tex] ( x2 , y2 )

Finding the slope :

Slope = [tex]\frac{y2-y1}{x2-x1}[/tex]

Slope = [tex]\frac{1 - ( -5 )}{4 - 1}[/tex]

Slope = [tex]\frac{1+5}{4-1}[/tex]

Slope = [tex]\frac{6}{3}[/tex]

Slope = [tex]2[/tex]

Hope I helped!

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~TheAnimeGirl

Which of the following results in the expression 0.22 ⋅ 86?

22 of 86%

22% of 86

86% of 0.22

0.86 of 22%

I need help plows pleasee!!

Answers

The answer is 22% of 86

Explanation:
0.22 is 22%
"of" means to multiply
86=86
22% of 86 hope that helped :))

Solve w - 4b = 1 for w

Answers

ISOLATE w

w-4b=1
+4b +4b
—————
w=1+4b

Answer: w=1+4b

solve for x
x/3 = 5/8​

Answers

Answer:

x = 15/8

Step-by-step explanation:

x/3 = 5/8

Using cross products

8x = 3*5

8x = 15

Divide each side by 8

8x/8 = 15/8

x = 15/8

X= 1 7/8

Step-by-step explanation:

choose the expression that completes the equation 33 / 3 + 10=_______


1. 2(10+1)

2. 10(1+1)

3. 3(6+1)

4 5(3+5)

Answers

Answer:

the answer is number 3. 3 ( 6+1 )

Number one would be your answer because 33/3+10 equals to 21 and 2(10+1) equals 21 as well.

Hope this helped

A baker has 3/4 pound of sugar left in his pantry he needs 1/8 of a pound for each batch of cookies ha make what is the greatest number of batches of cookies the baker can make with the 3/4 pound of sugar

Answers

Answer: 6

Step-by-step explanation:

If you convert 3/4 into eighths then it would be 6/8's so the baker can make 6 batches.

Which system of equations is equivalent to the following system?
4x + y = 4
2x + 7y = 28

Answers

Answer:

the third one

-28x-7y=-28

2x+7y=28

Step-by-step explanation:

for the first one, the 2x+7y=28 is being multiplied by -1, but its not being distributed correctly (28 is incorrect, it should be -28)

for the second one, the 2x+7y=28 is being multiplied by -4, but again, is not being distributed correctly (112 is incorrect, it should be -112)

for the fourth one, 4x+y=4 is being multiplied by -2, but its not being distributed correctly (8 is incorrect, it should be -8)

The system of equations equivalent to the given system is -28x -7y = -28, 2x + 7y = 28, the correct option is C.

What is System of Equation?

The system of equation is set of equations which have a common solution.

The system of equation is,

4x +y = 4

2x +7y =28

The equations can be solved using Substitution method, elimination method and by plotting the graph.

In substitution method, the value of one variable from an equation is substituted in the other equation.

4x +y = 4

y = 4 - 4x

This will be substituted in the equation 2

2x + 7 (4-4x) = 28

2x +28 - 28x  = 28

-26x = 0

x = 0

Putting this value in equation 1 , y = 4.

In elimination method, one of the variable is eliminated to solve the system of equation.

To eliminate y, the equation 1 will be multiplied by -7,

-28x -7y = -28

2x + 7y = 28

This is equivalent to the original system of equation.

Adding the equations will yield

-26x = 0

x = 0

y = 4.

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Find the range of the data in the box plot below.
Magnitude of earthquakes
0 1 2 3 4 5
6 7 8 9 10

What is the range?

Answers

The range of the given magnitude is 10.

What is Range?

The range is the difference between the largest value and the smallest value, is the simplest measure of variability in the data. The range is determined by only the two extreme data values.

Here, given data;

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Range = Upper limit - Lower limit

           = 10 - 0

           = 10

Thus, the range of the given magnitude is 10.

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Which of the following is a term?
A: 17y + 11
B: 6p
C: 7x / 2
D: 1 + 1

Answers

b: 6p is a term in this question

Answer:

B

Step-by-step explanation:

PLS SOLVE!! n+5 / -16 = -1

Answers

Answer:

The answer is n = 11.

Step-by-step explanation:

Answer:

n = 11

Step-by-step explanation:

n + 5 =  -1

 -16

n + 5 = -1 (-16)

n = 16 - 5

n = 11

rosa puts 2/3 cup of vegetables mixture in 1 tortilla. she has 8 cups of vegetable mixture.

Answers

she can fill 12 tortillas

Answer:

She need to divide 24 by 2 to get 12. She can fill 12 tortillas

Step-by-step explanation:

Evquivilent Ratio for 23:37

Answers

Answer:

46:74

Step-by-step explanation:

Divide 1/4÷2/3 and express the answer in the simplest terms. If necessary, use / for the fraction bar.

1/4 ÷ 2/3 =​

Answers

Answer:

3/8

Step-by-step explanation:

find the Least Common Denominator, change the numerators as needed, divide, then simplify.

Answer:

the answer is 3/8

Step-by-step explanation:

brainiest rate 5 stars and thank mee : )

Which expression can be used to find 80% of 120?

Answers

Answer: the expression (120/100)*80 results in 80% of 120

Step-by-step explanation:

) How many digits are in the number 13,692,540?​

Answers

8 Digits are in that number

Robert earned $10, which was 4 less than twice what Eric earned. How much money
did Eric earn?

Answers

Answer:

uh

Step-by-step explanation:

gygygyg

Solve please? Thanks :)

Answers

Answer:

Step-by-step explanation:

lol this was really funny

scientific notions have to be less than 10 and more than 1

1. 68600 / 10000 = 6.86

A. 6.86 x 10^4

2. 0.082 x 100 = 8.2

C. 8.2 x 10^-2

3. 0.068 x 100 = 6.8

D. 6.8 x 10^-2

4. 0.93 x 10 = 9.3

C. 9.3 x 10^-1

5. 0.000923 x 10000 = 9.23

D. 9.23 x 10^-5

Which of the following expressions are equivalent to -x/y

Answers

Answer:

-z/e

Step-by-step explanation:

-x/y = -z/e

Mary is twice as old as Helen’s age, If 8 is subtracted from Helen’s Age and 4 is added to Mary Age? Mary will be 4 times as old as Helen. What are the ages

Answers

Answer:

set mary is x years old, and helen is y years old.

first sentence:x=2y

second one:4(y-8)=x+4

bring x=2y in 4(y-8)=x+4

=>4y-32=2y+4

=>2y=36

=>y=18

=>x=36

mary:36

helen:18

We want to write and solve a system of equations that models given situation. We will see that Helen is 18 years old, and Mary is 36 years old.

Let's define the variables we will be using.

m = Mary's age.h = Helen's age.

We know that "Mary is twice as old as Helen’s age"

Then:

m = 2*h

"If 8 is subtracted from Helen’s Age and 4 is added to Mary Age, Mary will be 4 times as old as Helen."

(m + 4) = 4*(h - 8)

Then the system of equations is:

m = 2*h

(m + 4) = 4*(h - 8)

To solve it, we can replace m by 2*h in the second equation, so we get:

(2h + 4) = 4*(h - 8)

2*h + 4 = 4*h - 32

4 + 32 = 4*h - 2*h

36/2 = h = 18

And we know that:

m = 2*h = 2*18 = 36

So Helen is 18 years old, and Mary is 36 years old.

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The sum of the angle measures of a quadrilateral is 360°.
write and solve an equation to find the value of x. Use a protractor to check the
reasonableness of your answer.

Answers

Answer is x=31
125+132+72+x=360
329+x=360
x=31

A club elects a president, vice-president, and secretary-treasurer. How many sets of officers are possible if there are 11 members and any member can be elected to each position? No person can hold more than one
office

Answers

11 members and we have to pick three without replacement.

[tex]_{11} C_{3}[/tex] = 165

There are 165 possible sets of officers

Type your response in the box.
Janet and Patrick are buying stuffed frogs each month to give to a charity. Pattern 1 describes Janet's collection over
the first three months. Pattern 2 describes Patrick's collection. Study both patterns, and fill in the table based on
your observations.

Answers

Step-by-step explanation:

Pattern 1 :

Arithmetic Sequence

Common term = 4

Pattern 2 :

Geometric Sequence

Common ratio = 2

Answer:

pattern 1 arithmetic The common difference is 4. The pattern starts at 3 and always adds 4 to get to the next term.

pattern 2 geometric The common ratio is 2. The pattern starts at 3 and always multiplies by 2 to get to the next term.

Step-by-step explanation:

A carnival ride holds 30 people at a time. In one hour,
220 people went on the ride. It was full each time
except the last. How many times was the ride
completely filled?

Answers

Answer:

7

Step-by-step explanation:

The average of 5 distinct scores has the same value as
the median of the 5 scores. The sum of the 5 scores is
420. What is the sum of the 4 scores that are NOT the
median?

Answers

Answer:  336 is the sum of the non-median scores

Step-by-step explanation:  if the sum of 5 scores is 420, the average is 420/5 = 84  

That is also the median to be subtracted:  420-84= 336

I did this one slot of times but I never get it

Answers

Answer:

A: [tex]x^{2} \leq 16[/tex]

A is a solution set of the inequality.  

This means:

[tex]x^{2} \leq 4[/tex]

(AND)

[tex]x^{2} \geq -4[/tex]

Which can also be written as:

Interval notation: x ∈ [-4, 4]

Set notation:  {x | [tex]-4 \leq x \leq 4[/tex] }

Rewrite 10 7/8 as an improper fraction. I need help:)

Answers

Answer:87/8

Step-by-step explanation:cause i smart :D

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Write the equation of the line that has a slope of -5 and goes through (1,-4)

Answers

Answer:

y=-5x+1

Step-by-step explanation:

plug the coordinate points to the equation, and find your y intercept

Jade and Jackson are considering a $210,000 mortgage for 30 years at 5.7%. With this information, their monthly payment would be $1218.84.

If they make only the minimum payment each month, what is the total payback of this loan?

How much of this total payback is interest?

Answers

Answer:

Jade and Jackson

The total payback of this loan = $438,782.72

The interest of this total payback is $228,782.72

Step-by-step explanation:

a) Data and Calculations:

Mortgage = $210,000

Interest rate of mortgage = 5.7%

Monthly payment = $1,218.84

Using an online calculator for Mortgage Payoff, the Original Payoff Schedule  is:

Monthly Pay = $1,218.84

Total Payments = $438,782.72

Total Interest = $228,782.72

Answer:

Step-by-step explanation:

1218.84⋅12⋅30=$438,782.40

The total interest paid is the total payback less the amount borrowed.

$438,782.40−$210,000=$228,782.40

I have done this for a million times and I always get this one wrong I need the correct answer

Answers

Answer:

A, B, and D.

Step-by-step explanation:

HEY!! remember that if a number has ^2, it basically means it's multiplied by itself. for example:

5^2 = 5 x 5

aka, 25.

You can use this to check each of the answers in your formula, like this:

if x=6, then:

x^2 < 100

6 x 6 = 36

36 < 100

A is one of your correct answers!

Also remember, if you multiply a negative by a negative, it becomes positive.

-5 x -5 = 25

-10 x -10 = 100

The answer to this is A, B, D.
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