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If a single fair die is rolled find the probability of a 4

Question : If a single fair die is rolled find the probability of a 4 : 2151662

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

1) If a single fair die is rolled, find the probability of a 4 given that the number rolled is odd.

A) (1/6)

B) (1/2)

C) 0

D) 1

2) If a single fair die is rolled, find the probability of a 5 given that the number rolled is odd.

A) (2/3)

B) (1/6)

C) (1/2)

D) (1/3)

3) If two fair dice are rolled, find the probability of a sum of 6 given that the roll is a double.

A) (1/5)

B) (1/6)

C) (1/4)

D) (1/3)

4) If two fair dice are rolled, find the probability that the roll is a double given that the sum is 11.

A) (1/4)

B) (1/3)

C) (1/2)

D) 0

5) If two cards are drawn without replacement from an ordinary deck, find the probability that the second card is a spade, given that the first card was a spade.

A) (3/13)

B) (11/12)

C) (4/17)

D) (11/51)

6) If two cards are drawn without replacement from an ordinary deck, find the probability that the second card is red, given that the first card was a heart.

A) (4/17)

B) (26/51)

C) (22/23)

D) (25/51)

7) If two cards are drawn without replacement from an ordinary deck, find the probability that the second card is a face card, given that the first card was a queen.

A) (4/17)

B) (3/13)

C) (11/51)

D) (5/17)

8) If two cards are drawn without replacement from an ordinary deck, find the probability that the second card is an ace, given that the first card was an ace.

A) (3/52)

B) (1/17)

C) (4/51)

D) (1/3)

9) If three cards are drawn without replacement from an ordinary deck, find the probability that the third card is a heart, given that the first two cards were hearts.

A) (1/5)

B) (6/25)

C) (1/6)

D) (11/50)

10) If three cards are drawn without replacement from an ordinary deck, find the probability that the third card is a face card, given that the first card was a queen and the second card was a 5.

A) (3/13)

B) (6/25)

C) (11/50)

D) (1/5)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

11) In a local election, 56.0% of those aged under 40 and 48.8% of those aged over 40 vote in favor of a certain ballot measure. Are age and "voting in favor" independent? How can you tell?

12) Let A be the event that it will be sunny this afternoon.

Let B be the event that Francia will go shopping this afternoon. Given that P(A) = 0.8, P(B) = 0.7, and P(A∩B) = 0.2, are events A and B independent? How can you tell?

13) A card is drawn at random from a well-shuffled deck of 52 cards.

Let A be the event that the card is a heart.

Let B be the event that the card is a king.

Find P(A), P(B), and P(A∩B). Are events A and B independent? How can you tell?

14) When a coin is tossed three times, eight equally likely outcomes are possible.

HHH HHT HTH HTT

THH THT TTH TTT

Let

A = event the first two tosses are the same

B = event the last two tosses are the same.

Find P(A), P(B), and P(A∩B).

Are A and B independent events? How can you tell?

15) When a balanced die is rolled twice, 36 equally likely outcomes are possible. Let

A = event the sum of the two rolls is 8

B = event the first roll comes up 3.

Find P(A) and P(A|B).

Are A and B independent events? How can you tell?

16) The following contingency table provides a joint frequency distribution for the popular votes cast in the 1984 presidential election by region and political party. Data are in thousands, rounded to the nearest thousand.

Political Party

A person who voted in the 1984 presidential election is selected at random.

Find the probability that the person voted Republican.

Find the probability that the person voted Republican given that they are from the South.

Are the events "voting Republican" and "being from the South" independent? How can you tell?

17) The following contingency table provides a joint frequency distribution for a group of retired people by career and age at retirement.

Age at Retirement

Suppose one of these people is selected at random. Find the probability that the person selected was an attorney. Then find the probability that the person selected was an attorney given that the person retired between 61 and 65. Are the events "attorney" and "retirement between 61 and 65" independent? How can you tell?

18) The table below describes the smoking habits of a group of asthma sufferers.

If one of the 1038 subjects is randomly selected, find P(N), the probability that the person is a nonsmoker. Then find P(N|W), the probability that the person chosen is a nonsmoker given that the person is a woman.

Are the events "being a nonsmoker" and "being a woman" independent? How can you tell?

19) The table below describes the smoking habits of a group of asthma sufferers.

If one of the 1038 subjects is randomly selected, find P(H), the probability that the person is a heavy smoker. Then find P(M), the probability that the person chosen is a man. Then find P(H∩M), the probability that the person is a heavy smoker and a man.

Are the events "being a heavy smoker" and "being a man" independent? How can you tell?

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the indicated probability.

20) Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. Find the probability that both marbles are red.

A) (3/56)

B) (1/16)

C) (1/28)

D) (1/4)

21) Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. Find the probability that both marbles are white.

A) (3/28)

B) (3/32)

C) (3/8)

D) (9/56)

22) Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. Find the probability that both marbles are green.

A) (1/4)

B) (1/16)

C) (1/28)

D) (1/14)

23) Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. Find the probability that the first marble is white and the second marble is blue.

A) (3/28)

B) (3/64)

C) (3/56)

D) (29/56)

24) Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. Find the probability that one marble is green, and one marble is red.

A) (1/2)

B) (1/4)

C) (3/28)

D) (1/7)

25) You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that both cards are black.

A) (1/2652)

B) (25/51)

C) (13/51)

D) (25/102)

26) You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that the first card is a king and the second card is a queen.

A) (1/663)

B) (4/663)

C) (2/13)

D) (13/102)

Find the probability.

27) If 81% of scheduled flights actually take place and cancellations are independent events, what is the probability that 3 separate flights will all take place?

A) 0.66

B) 0.53

C) 0.81

D) 0.01

28) A calculator requires a keystroke assembly and a logic circuit. Assume that 94% of the keystroke assemblies and 81% of the logic circuits are satisfactory. Find the probability that a finished calculator will be satisfactory. Assume that defects in keystroke assemblies are independent of defects in logic circuits.

A) 0.7614

B) 0.8836

C) 0.8800

D) 0.6561

29) If two cards are drawn with replacement from an ordinary deck, find the probability the first card is a heart and the second is a diamond.

A) (1/204)

B) (1/16)

C) (13/204)

D) (1/169)

30) A family has five children. The probability of having a girl is 1/2. What is the probability of having 2 girls followed by 3 boys? Round your answer to four decimal places.

A) 0.1875

B) 0.6252

C) 0.0313

D) 0.3125

31) A basketball player hits her shot 44% of the time. If she takes four shots during a game, what is the probability that she misses the first shot and hits the last three? Express the answer as a percentage, and round to the nearest tenth (if necessary). Assume independence of shots.

A) 37.5%

B) 4.8%

C) 3.7%

D) 47.7%

32) Find the probability of correctly answering the first 3 questions on a multiple choice test if random guesses are made and each question has 6 possible answers.

A) 2

B) (1/2)

C) (1/729)

D) (1/216)

33) A batch consists of 12 defective coils and 88 good ones. Find the probability of getting two good coils when two coils are randomly selected if the first selection is replaced before the second is made.

A) 0.7744

B) 0.0144

C) 0.176

D) 0.7733

34) When a pair of dice is rolled there are 36 different possible outcomes: 1-1, 1-2, ¼, 6-6. If a pair of dice is rolled 3 times, what is the probability of getting a sum of 3 every time?

A) 0.1111

B) 0.0005787

C) 0.00017147

D) 0.03703704

35) In one town, 60% of adults have health insurance. What is the probability that 4 adults selected at random from the town all have health insurance?

A) 0.067

B) 2.4

C) 0.13

D) 0.6

36) Find the probability that 3 randomly selected people all have the same birthday. Ignore leap years.

A) 0.3333

B) 0.0082

C) 0.00000002

D) 0.00000751

Solution
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