Question 1

Let A and B be events in a sample space S such that  ,  , and  . Find:  . ​

Accepted Answer

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

Question 2

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

Accepted Answer

Without any additional information about the events, we cannot definitively determine independence.

Question 3

Assume that the probability of a boy being born is the same as the probability of a girl being born. Find the probability that a family with four children will have the given composition. Give your answer in the form of a fraction.
​
Exacty two boys.

Accepted Answer

The answer of Assume that the probability of a boy...

Question 4

Let A and B be events in a sample space S such that  and  . Find:  . ​

Accepted Answer

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

Question 5

An unbiased coin is tossed seven times. Find the probability of the given event. Give your answer in the form of a fraction.
​
The coin lands heads at least once.

Accepted Answer

The answer of An unbiased coin is tossed seven times....

Question 6

Fourty people are selected at random. What is the probability that none of the people in this group have the same birthday? Round your answer to the nearest hundredth, if necessary.
​
The probability is __________.

Accepted Answer

The answer of Fourty people are selected at random. What...

Question 7

There were 42 different presidents of the United States from 1789 through 2000. What is the probability that at least four of them had the same birthday? Round your answer to six decimal places, if necessary.
​
The probability is __________.

Accepted Answer

The answer of There were 42 different presidents of the...

Question 8

The City Transit Authority plans to hire 12 new bus drivers. From a group of 200 qualified applicants, of which 180 are men and 20 are women, 12 names are to be selected by lot. Suppose that Mary and John Lewis are among the 200 qualified applicants.
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What is the probability that Mary's name will be selected?
​
__________
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What is the probability that both Mary's and John's names will be selected?
​
__________
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It is stipulated that an equal number of men and women are to be selected (6 men from the group of 180 men and 6 women from the group of 20 women)
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What is the probability that Mary's name will be selected?
​
__________
​
What is the probability that Mary's and John's names will be selected?
​
__________

Accepted Answer

The answer of The City Transit Authority plans to hire...

Question 9

What is the probability that at least two of the nine justices of the U.S. Supreme Court have the same birthday? Round your answer to four decimal places, if necessary.
The probability is __________.

Accepted Answer

The answer of What is the probability that at least...

Question 10

A druggist wishes to select three brands of aspirin to sell in his store. He has five major brands to choose from: A, B, C, D, and E. If he selects the three brands at random, what is the probability that he will select brand E? Give your answer in the form of a fraction.

Accepted Answer

The answer of A druggist wishes to select three brands...

Question 11

Four balls are selected at random without replacement from an urn containing three white balls and five blue balls. Find the probability of the given event. Give your answer in the form of a fraction.
​
Exactly three of the balls are blue.

Accepted Answer

The answer of Four balls are selected at random without...

Question 12

A list of poker hands ranked in order from the highest to the lowest is shown in the table, along with a description and example of each hand. Use the table to answer the problem.
​  ​
If a 5-card poker hand is dealt from a well-shuffled deck of 52 cards, what is the probability of being dealt a flush?
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Round your answer to five decimal places, if necessary.
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The probability is __________.

Accepted Answer

The answer of A list of poker hands ranked in...

Question 13

A shelf in the Metro Department Store contains 75 colored ink cartridges for a popular ink-jet printer. Seven of the cartridges are defective. A customer selects 2 of these cartridges at random from the shelf.
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What is the probability that both are defective?
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__________
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What is the probability that at least 1 is defective?
​
__________

Accepted Answer

The answer of A shelf in the Metro Department Store...

Question 14

In "The Numbers Game," a state lottery, four numbers are drawn with replacement from an urn containing the digits 0-9, inclusive.
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Find the probability of a ticket holder having the winning ticket with all four digits in any order (including the other winning tickets). Assume that there are 2 pairs of the same digits.
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Give your answer in the form of a fraction.

Accepted Answer

The answer of In "The Numbers Game," a state lottery,...

Question 15

Assume that the probability of a boy being born is the same as the probability of a girl being born. Find the probability that a family with five children will have at least one boy.

Accepted Answer

The answer of Assume that the probability of a boy...

Question 16

Let A and B be events in a sample space S such that  ,  , and  . Find:  . ​

Accepted Answer

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

Question 17

In "The Numbers Game", a state lottery, four numbers are drawn with replacement from an urn containing the digits 0-9, inclusive. Find the probability of a ticket holder having the indicated winning ticket.
​
All four digits in exact order(the grand prize)
​
The probability is __________.

Accepted Answer

The answer of In "The Numbers Game", a state lottery,...

Question 18

A "lucky dollar" is one of the nine symbols printed on each reel of a slot machine with three reels. A player receives one of various payouts whenever one or more "lucky dollars" appear in the window of the machine.
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What is the probability that exactly two "lucky dollar" symbols will appear in the window of the slot machine? Give your answer in the form of a fraction.

Accepted Answer

The answer of A "lucky dollar" is one of the...

Question 19

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

Accepted Answer

Two events A and B are independent if and only if the occurrence of one event does not affect the probability of the other event. In this case, since the events have the same prefix "11eab448_e7e2_", it is likely that they are related and therefore not independent.

Question 20

In the game of blackjack, a 2-card hand consisting of an ace and a face card or a 10 is called a blackjack. Give the answers to four decimal places.
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If a player is dealt 2 cards from a standard deck of 52 well-shuffled cards, what is the probability that the player will receive a blackjack?
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__________
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If a player is dealt 2 cards from 7 well-shuffled standard decks, what is the probability that the player will receive a blackjack?
​
__________

Accepted Answer

The answer of In the game of blackjack, a 2-card...

Quiz 7: Probability

Let A and B be events in a sample space S such that , , and . Find: .

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

Assume that the probability of a boy being born is the same as the probability of a girl being born. Find the probability that a family with four children will have the given composition. Give your answer in the form of a fraction. Exacty two boys.

Let A and B be events in a sample space S such that and . Find: .

An unbiased coin is tossed seven times. Find the probability of the given event. Give your answer in the form of a fraction. The coin lands heads at least once.

Fourty people are selected at random. What is the probability that none of the people in this group have the same birthday? Round your answer to the nearest hundredth, if necessary. The probability is __________.

There were 42 different presidents of the United States from 1789 through 2000. What is the probability that at least four of them had the same birthday? Round your answer to six decimal places, if necessary. The probability is __________.

What is the probability that at least two of the nine justices of the U.S. Supreme Court have the same birthday? Round your answer to four decimal places, if necessary. The probability is __________.

A druggist wishes to select three brands of aspirin to sell in his store. He has five major brands to choose from: A, B, C, D, and E. If he selects the three brands at random, what is the probability that he will select brand E? Give your answer in the form of a fraction.

Four balls are selected at random without replacement from an urn containing three white balls and five blue balls. Find the probability of the given event. Give your answer in the form of a fraction. Exactly three of the balls are blue.

Assume that the probability of a boy being born is the same as the probability of a girl being born. Find the probability that a family with five children will have at least one boy.

Let A and B be events in a sample space S such that , , and . Find: .

In "The Numbers Game", a state lottery, four numbers are drawn with replacement from an urn containing the digits 0-9, inclusive. Find the probability of a ticket holder having the indicated winning ticket. All four digits in exact order(the grand prize) The probability is __________.

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

Quiz 7: Probability

Let A and B be events in a sample space S such that , , and . Find: . ​

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

Assume that the probability of a boy being born is the same as the probability of a girl being born. Find the probability that a family with four children will have the given composition. Give your answer in the form of a fraction. ​ Exacty two boys.

Let A and B be events in a sample space S such that and . Find: . ​

An unbiased coin is tossed seven times. Find the probability of the given event. Give your answer in the form of a fraction. ​ The coin lands heads at least once.

Fourty people are selected at random. What is the probability that none of the people in this group have the same birthday? Round your answer to the nearest hundredth, if necessary. ​ The probability is __________.

There were 42 different presidents of the United States from 1789 through 2000. What is the probability that at least four of them had the same birthday? Round your answer to six decimal places, if necessary. ​ The probability is __________.

What is the probability that at least two of the nine justices of the U.S. Supreme Court have the same birthday? Round your answer to four decimal places, if necessary. The probability is __________.

A druggist wishes to select three brands of aspirin to sell in his store. He has five major brands to choose from: A, B, C, D, and E. If he selects the three brands at random, what is the probability that he will select brand E? Give your answer in the form of a fraction.

Four balls are selected at random without replacement from an urn containing three white balls and five blue balls. Find the probability of the given event. Give your answer in the form of a fraction. ​ Exactly three of the balls are blue.

Assume that the probability of a boy being born is the same as the probability of a girl being born. Find the probability that a family with five children will have at least one boy.

Let A and B be events in a sample space S such that , , and . Find: . ​

In "The Numbers Game", a state lottery, four numbers are drawn with replacement from an urn containing the digits 0-9, inclusive. Find the probability of a ticket holder having the indicated winning ticket. ​ All four digits in exact order(the grand prize) ​ The probability is __________.

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

Let A and B be events in a sample space S such that , , and . Find: .

Assume that the probability of a boy being born is the same as the probability of a girl being born. Find the probability that a family with four children will have the given composition. Give your answer in the form of a fraction. Exacty two boys.

Let A and B be events in a sample space S such that and . Find: .

An unbiased coin is tossed seven times. Find the probability of the given event. Give your answer in the form of a fraction. The coin lands heads at least once.

Fourty people are selected at random. What is the probability that none of the people in this group have the same birthday? Round your answer to the nearest hundredth, if necessary. The probability is __________.

There were 42 different presidents of the United States from 1789 through 2000. What is the probability that at least four of them had the same birthday? Round your answer to six decimal places, if necessary. The probability is __________.

Four balls are selected at random without replacement from an urn containing three white balls and five blue balls. Find the probability of the given event. Give your answer in the form of a fraction. Exactly three of the balls are blue.

Let A and B be events in a sample space S such that , , and . Find: .

In "The Numbers Game", a state lottery, four numbers are drawn with replacement from an urn containing the digits 0-9, inclusive. Find the probability of a ticket holder having the indicated winning ticket. All four digits in exact order(the grand prize) The probability is __________.