Question 1

If A and B are independent events,  , and  , find  . Give the answer to two decimal places, if necessary.
​  __________

Accepted Answer

The answer of If A and B are independent events,...

Question 2

Let A and B be events in a sample space S such that  ,  , and  . Find:  . Give the answer to two decimal places, if necessary.
​  __________

Accepted Answer

The answer of Let A and B be events in...

Question 3

A card is drawn from a well-shuffled deck of 36 playing cards. Let E denote the event that the card drawn is red and let F denote the event that the card drawn is a diamond. Determine whether E and F are dependent events. Answer dependent or independent.

Accepted Answer

The answer of A card is drawn from a well-shuffled...

Question 4

Let A and B be events in a sample space S such that  ,  , and  . Find:  . Give the answer to two decimal places, if necessary.
​  __________

Accepted Answer

The answer of Let A and B be events in...

Question 5

Let A and B be events in a sample space S such that  and  . Find:  . Give the answer to two decimal places, if necessary.
​  __________

Accepted Answer

The answer of Let A and B be events in...

Question 6

If A and B are independent events,  , and  , find  . Give the answer to two decimal places, if necessary.
​  __________

Accepted Answer

The answer of If A and B are independent events,...

Question 7

Three cards are drawn without replacement from a well-shuffled deck of 52 playing cards. What is the probability that the third card drawn is a diamond? Give the answer to two decimal places, if necessary.
​
The probability is __________.

Accepted Answer

The answer of Three cards are drawn without replacement from...

Question 8

A pair of fair dice is cast. Let E denote the event that the number landing uppermost on the first die is a 1 and let F denote the event that the sum of the numbers falling uppermost is 2. Determine whether E and F are independent events. Answer dependent or independent.

Accepted Answer

The answer of A pair of fair dice is cast....

Question 9

Determine whether the given events A and B are independent.  ,  , and  . Answer dependent or independent.

Accepted Answer

The answer of Determine whether the given events A and...

Question 10

A tax specialist has estimated the probability that a tax return selected at random will be audited is .02. Furthermore, he estimates the probability that an audited return will result in additional assessments being levied on the taxpayer is .50.
​
What is the probability that a tax return selected at random will result in additional assessments being levied on the taxpayer? Give the answer to three decimal places, if necessary.
​
The probability is __________.

Accepted Answer

The answer of A tax specialist has estimated the probability...

Question 11

Determine whether the given events A and B are independent.  ,  , and  . Answer dependent or independent.

Accepted Answer

The answer of Determine whether the given events A and...

Question 12

The proprietor of Cunningham's Hardware Store has decided to install floodlights on the premises as a measure against vandalism and theft.
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If the probability is 0.01 that a certain brand of floodlight will burn out within a year, find the minimum number of floodlights that must be installed to ensure that the probability that at least one of them will remain functional within the year is at least 0.9999. (Assume that the floodlights operate independently.)
​
The probability is __________.

Accepted Answer

The answer of The proprietor of Cunningham's Hardware Store has...

Question 13

A box contains two defective Christmas tree lights that have been inadvertently mixed with eleven nondefective lights. If the lights are selected one at a time without replacement and tested until both defective lights are found, what is the probability that both defective lights will be found after three trials? Give your answer in fraction form.

Accepted Answer

The answer of A box contains two defective Christmas tree...

Question 14

Suppose E and F are mutually exclusive events and P(E∪F) ≠ 0. What is P(E|E∪F)? ​
A) 
B) 1
C) 0
D) 
E)

Accepted Answer

P(E|E∪F) = P(E∩(E∪F))/P(E∪F)
Since E and F are mutually exclusive, E∩F = ∅.
So, E∩(E∪F) = E.
Therefore, P(E|E∪F) = P(E)/P(E∪F)
Since P(E∩F) = ∅, P(E∪F) = P(E) + P(F).
Since P(E∪F) ≠ 0, P(E) ≠ 0 and P(F) ≠ 0.
Since E and F are mutually exclusive, P(E∩F) = ∅, which means P(E) + P(F) = P(E) + 0 or P(E) + P(F) = 0 + P(F). In either case, P(E∪F) = P(E) + P(F) = P(E) + 0 or P(E) + P(F) = 0 + P(F) = P(F).
Thus, P(E∪F) = P(E) + P(F) = P(E) or P(E∪F) = P(F).
So, P(E|E∪F) = P(E)/P(E∪F) = P(E)/P(E) = 1.

Question 15

A coin is tossed 4 times.
​
Give your answers in fraction form.
​
What is the probability that the coin will land heads at least twice?
​
__________
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What is the probability that the coin will land heads on the third toss given that heads were thrown on the first toss?
​
__________
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What is the probability that the coin will land heads on the fourth toss given that tails were thrown on the first toss?
​
__________

Accepted Answer

The answer of A coin is tossed 4 times.
​
Give your...

Question 16

A pair of fair dice is cast. What is the probability that the sum of the numbers falling uppermost is less than 8, if it is known that one of the numbers is a 4? Give your answer in fraction form.

Accepted Answer

The answer of A pair of fair dice is cast....

Question 17

The probability that a battery will last 8 hr or more is .50, and the probability that it will last 17 hr or more is .9. Given that a battery has lasted 8 hr, find the probability that it will last 17 hr or more. Give the answer to three decimal places, if necessary.
​
The probability is __________.

Accepted Answer

The answer of The probability that a battery will last...

Question 18

A nationwide survey conducted by the National Cancer Society revealed the following information: Of 10,000 people surveyed, 3,500 were "heavy coffee drinkers" and 160 had cancer of the pancreas. Of those who had cancer of the pancreas, 141 were heavy coffee drinkers.
Using the data in this survey, determine whether the events "being a heavy coffee drinker" and "having cancer of the pancreas" are independent events. Answer independent or not independent.

Accepted Answer

The answer of A nationwide survey conducted by the National...

Question 19

Suppose A and C are mutually exclusive events and P(A|C) ≠ 0. What is P(A|A∪C)?

Accepted Answer

The answer of Suppose A and C are mutually exclusive...

Question 20

Seven black balls and five white balls are placed in an urn. Two balls are then drawn in succession.
​
Give your answers in fraction form.
​
What is the probability that the second ball drawn is a white ball if the second ball is drawn without replacing the first?
​
__________
​
What is the probability that the second ball drawn is a white ball if the first ball is replaced before the second is drawn?
​
__________

Accepted Answer

The answer of Seven black balls and five white balls...

Quiz 7: Probability

If A and B are independent events, , and , find . Give the answer to two decimal places, if necessary. __________

Let A and B be events in a sample space S such that , , and . Find: . Give the answer to two decimal places, if necessary. __________

A card is drawn from a well-shuffled deck of 36 playing cards. Let E denote the event that the card drawn is red and let F denote the event that the card drawn is a diamond. Determine whether E and F are dependent events. Answer dependent or independent.

Let A and B be events in a sample space S such that , , and . Find: . Give the answer to two decimal places, if necessary. __________

Let A and B be events in a sample space S such that and . Find: . Give the answer to two decimal places, if necessary. __________

If A and B are independent events, , and , find . Give the answer to two decimal places, if necessary. __________

Three cards are drawn without replacement from a well-shuffled deck of 52 playing cards. What is the probability that the third card drawn is a diamond? Give the answer to two decimal places, if necessary. The probability is __________.

A pair of fair dice is cast. Let E denote the event that the number landing uppermost on the first die is a 1 and let F denote the event that the sum of the numbers falling uppermost is 2. Determine whether E and F are independent events. Answer dependent or independent.

Determine whether the given events A and B are independent. , , and . Answer dependent or independent.

Determine whether the given events A and B are independent. , , and . Answer dependent or independent.

Suppose E and F are mutually exclusive events and P(E∪F) ≠ 0. What is P(E|E∪F) ?

A pair of fair dice is cast. What is the probability that the sum of the numbers falling uppermost is less than 8, if it is known that one of the numbers is a 4? Give your answer in fraction form.

The probability that a battery will last 8 hr or more is .50, and the probability that it will last 17 hr or more is .9. Given that a battery has lasted 8 hr, find the probability that it will last 17 hr or more. Give the answer to three decimal places, if necessary. The probability is __________.

Suppose A and C are mutually exclusive events and P(A|C) ≠ 0. What is P(A|A∪C)?

Quiz 7: Probability

If A and B are independent events, , and , find . Give the answer to two decimal places, if necessary. ​ __________

Let A and B be events in a sample space S such that , , and . Find: . Give the answer to two decimal places, if necessary. ​ __________

A card is drawn from a well-shuffled deck of 36 playing cards. Let E denote the event that the card drawn is red and let F denote the event that the card drawn is a diamond. Determine whether E and F are dependent events. Answer dependent or independent.

Let A and B be events in a sample space S such that , , and . Find: . Give the answer to two decimal places, if necessary. ​ __________

Let A and B be events in a sample space S such that and . Find: . Give the answer to two decimal places, if necessary. ​ __________

If A and B are independent events, , and , find . Give the answer to two decimal places, if necessary. ​ __________

Three cards are drawn without replacement from a well-shuffled deck of 52 playing cards. What is the probability that the third card drawn is a diamond? Give the answer to two decimal places, if necessary. ​ The probability is __________.

A pair of fair dice is cast. Let E denote the event that the number landing uppermost on the first die is a 1 and let F denote the event that the sum of the numbers falling uppermost is 2. Determine whether E and F are independent events. Answer dependent or independent.

Determine whether the given events A and B are independent. , , and . Answer dependent or independent.

Determine whether the given events A and B are independent. , , and . Answer dependent or independent.

Suppose E and F are mutually exclusive events and P(E∪F) ≠ 0. What is P(E|E∪F) ? ​

A pair of fair dice is cast. What is the probability that the sum of the numbers falling uppermost is less than 8, if it is known that one of the numbers is a 4? Give your answer in fraction form.

Suppose A and C are mutually exclusive events and P(A|C) ≠ 0. What is P(A|A∪C)?

If A and B are independent events, , and , find . Give the answer to two decimal places, if necessary. __________

Let A and B be events in a sample space S such that , , and . Find: . Give the answer to two decimal places, if necessary. __________

Let A and B be events in a sample space S such that , , and . Find: . Give the answer to two decimal places, if necessary. __________

Let A and B be events in a sample space S such that and . Find: . Give the answer to two decimal places, if necessary. __________

If A and B are independent events, , and , find . Give the answer to two decimal places, if necessary. __________

Three cards are drawn without replacement from a well-shuffled deck of 52 playing cards. What is the probability that the third card drawn is a diamond? Give the answer to two decimal places, if necessary. The probability is __________.

Suppose E and F are mutually exclusive events and P(E∪F) ≠ 0. What is P(E|E∪F) ?