Deck 9: Probability

Question 1

P ( A or B ) means which of the following?

A) P ( A ) P ( B )
B) P ( A ) P ( B )
C) P ( A B )
D) P ( A ) + P ( B )
E) P ( A B )

Answer 1

C

Question 2

Last year, 1,328 calculators were returned to the manufacturer. If 79,000 were produced, assign a number to specify the probability that a particular calculator would be returned. Give the probability in decimal form (correct to two decimal places). __________

Answer 2

0.02

Question 3

FIGURE 2. Refer to Figure 2. Use the sample space shown in the figure to find the probability of rolling two dice and having the sum be even. Give the answer as an exact fraction. P (even)

A) P (even) =
B) P (even) =
C) P (even) =
D) P (even) =
E) P (even) =

Answer 3

A

Question 4

The game of Dungeons and Dragons uses nonstandard dice. Consider a die with eight sides marked 1, 2, 3, 4, 5, 6, 7, and 8. (In this problem, "an eight" refers to rolling an eight on either or both dice, while "a total of eight" refers to the sum on the two dice.) List the sample space for yourself in order to answer the following question. What is the probability of rolling exactly one seven with two such dice?

A)
B)
C)
D)
E)

Question 5

In a game of dice, a player loses if the outcome of the first roll is a two, three, or twelve. (This refers to the total of the two dice.) What is the probability of a total of three on the first roll?

A)
B)
C)
D)
E)

Question 6

Suppose you flip 3 coins simultaneously. List the sample space for yourself in order to answer the question. What is the probability of all 3 coins being heads?

A)
B)
C)
D)
E)

Question 7

P ( A and B ) means which of the following?

A) P ( A ) P ( B )
B) P ( A B )
C) P ( A B )
D) P ( A ) + P ( B )
E) P ( A ) P ( B )

Question 8

FIGURE 1. Refer to Figure 1. Suppose that you toss a coin and roll a die. The sample space is shown in the figure. What is the probability of obtaining tails?

A) P (Tails) =
B) P (Tails) =
C) P (Tails) =
D) P (Tails) =
E) P (Tails) =

Question 9

For the spinners in the figure below, assume that the pointer can never lie on a border line. Find

A)
B)
C)
D)
E)

Question 10

FIGURE 1. Refer to Figure 1. Suppose that you toss a coin and roll a die. The sample space is shown in the figure. What is the probability of obtaining heads and a two?

A)
B)
C)
D)
E)

Question 11

Poker is a common game in which players are dealt five cards from a deck of cards. It can be shown that there are 2,598,960 different possible poker hands. The winning hands (from highest to lowest) are shown in the table below. Royal Flush 4 hands Other straight flush 36 hands Four of a kind 624 hands Full house 3,744 hands Flush 5,108 hands Straight 10,200 hands Three of a kind 54,912 hands Two pair 123,552 hands One pair 1,098,240 hands Other hands 1,302,540 hands Find the requested probabilities. Use a calculator. Select the pair of answers closest to the answers on your calculator. P (royal flush) __________ P (straight flush) __________

A) P (royal flush) 0.0000015; P (straight flush) 0.0000139
B) P (royal flush) 0.0000002; P (straight flush) 0.0000014
C) P (royal flush) 0.0000015; P (straight flush) 0.0000014
D) P (royal flush) 0.0000002; P (straight flush) 0.0000139
E) P (royal flush) 0.0000139; P (straight flush) 0.0000015

Question 12

Last year in Ferndale, CA, it rained on 28 days. What is the probability of rain on a day selected at random? Give the probability in decimal form (correct to two decimal places).

A) about
B) about
C) about
D) about
E) about

Question 13

Dice is a popular game in gambling casinos. Two dice are tossed, and various amounts are paid according to the outcome. If a seven or eleven occurs on the first roll, the player wins. If a player tosses a pair of ones (called snake eyes ) on the first roll, the player loses. What is the probability of tossing a seven on the first roll?

A)
B)
C)
D)
E)

Question 14

FIGURE 2. Refer to Figure 2. Use the sample space shown in the figure to find the probability of rolling two dice that add to seven: Give the answer as an exact fraction.

A)
B)
C)
D)
E)

Question 15

A single card is selected from an ordinary deck of cards. The sample space is shown in the figure below. Find the probability P ( red face card )

A)
B)
C)
D)
E)

Question 16

Last year, 1,394 calculators were returned to the manufacturer. If 72,000 were produced, assign a number to specify the probability that a particular calculator would be returned. Give the probability in decimal form (correct to two decimal places).

A) about
B) about
C) about
D) about
E) about

Question 17

If you simultaneously toss a coin and roll a die, the possible outcomes are H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, and T6. What is the probability of a head and an odd number?

A)
B)
C)
D)
E)

Question 18

FIGURE 2. Refer to Figure 2. Use the sample space shown in the figure to find the probability of rolling two dice that add to five: Give the answer as an exact fraction.

A)
B)
C)
D)
E)

Question 19

The campus vets club is having a raffle and is selling 3,000 tickets. If the people on the floor of your dorm bought 360 tickets, what is the probability that someone on your floor will hold the winning ticket? Give the probability in decimal form (correct to two decimal places).

A) about
B) about
C) about
D) about
E) about

Question 20

Last year, a certain professor gave 44 F grades out of 882 grades. If one of the professor's students were selected randomly, what is the probability of the student receiving an F? Give the probability in decimal form (correct to two decimal places).

A) about
B) about
C) about
D) about
E) about

Question 21

Last year in Ferndale, CA, it rained on 41 days. What is the probability of rain on a day selected at random? Give the probability in decimal form (correct to two decimal places). __________

Question 22

Last year, a certain professor gave 59 A grades out of 849 grades. If one of the professor s students were selected randomly, what is the probability of the student receiving an A? Give the probability in decimal form (correct to two decimal places). __________

Question 23

For the spinners in the figure below, assume that the pointer can never lie on a border line. Find Give your answer as a fraction.

Question 24

FIGURE 1. Refer to Figure 1. Suppose that you toss a coin and roll a die. The sample space is shown in the figure. What is the probability of obtaining tails or a five? Give your answer as a fraction.

Question 25

Suppose you flip 3 coins simultaneously. List the sample space for yourself in order to answer the question. What is the probability of all 3 coins being tails? Give your answer as a fraction.

Question 26

In a game of dice, a player loses if the outcome of the first roll is a two, three, or twelve. (This refers to the total of the two dice.) What is the probability of losing on the first roll? Give your answer as a fraction.

Question 27

Dice is a popular game in gambling casinos. Two dice are tossed, and various amounts are paid according to the outcome. If a seven or eleven occurs on the first roll, the player wins. If a player tosses a pair of ones (called snake eyes ) on the first roll, the player loses. What is the probability of winning on the first roll?
Give your answer as a fraction.

Question 28

FIGURE 2. Refer to Figure 2. Use the sample space shown in the figure to find the probability of rolling two dice that add to eight: Give your answer as a fraction.

Question 29

FIGURE 3. Refer to Figure 3. Suppose you and an opponent both pick one of the spinners in the figure. A win means spinning a higher number. Based on the probability of a win, which of the two spinners would you choose? plays __________ (Answer C , A , or either; it s a draw)

Question 30

FIGURE 3. Refer to Figure 3. Suppose you and an opponent both pick one of the spinners in the figure. A win means spinning a higher number. Based on the probability of a win, which of the two spinners would you choose? plays __________ (Answer F , D or either; it s a draw )

Question 31

FIGURE 1. Refer to Figure 1. Suppose that you toss a coin and roll a die. The sample space is shown in the figure. What is the probability of obtaining tails? Give your answer as a fraction.

Question 32

The campus vets club is having a raffle and is selling 2,500 tickets. If the people on the floor of your dorm bought 495 tickets, what is the probability that someone on your floor will hold the winning ticket? Give the probability in decimal form (correct to two decimal places). __________

Question 33

The game of Dungeons and Dragons uses nonstandard dice. Consider a die with eight sides marked 1, 2, 3, 4, 5, 6, 7, and 8. (In this problem, "an eight" refers to rolling an eight on either or both dice, while "a total of eight" refers to the sum on the two dice.) What is the probability of rolling exactly one two with two such dice?
Give your answer as a fraction.

Question 34

For the spinners in the figure below, assume that the pointer can never lie on a border line. Find Give your answer as a fraction.

Question 35

Suppose you simultaneously toss a coin and roll a die. The possible outcomes are H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, and T6. What is the probability of a three? Give your answer as a reduced fraction.

Question 36

Consider the following statement.
Answer true or false . P ( A or B ) means P ( A B )

Question 37

FIGURE 2. Refer to Figure 2. Use the sample space shown in the figure to find the probability of rolling two dice and having the sum be four or five: Give your answer as a fraction.

Question 38

Consider the following statement.
Answer true or false . P ( A and B ) means P ( A B )

Question 39

Poker is a common game in which players are dealt five cards from a deck of cards. It can be shown that there are 2,598,960 different possible poker hands. The winning hands (from highest to lowest) are shown in the table below. Royal flush 4 hands Other straight flush 36 hands Four of a kind 624 hands Full house 3,744 hands Flush 5,108 hands Straight 10,200 hands Three of a kind 54,912 hands Two pair 123,552 hands One pair 1,098,240 hands Other hands 1,302,540 hands Find the requested probabilities. Use a calculator and show your answers to whatever accuracy possible on your calculator. P (two pair) = __________ P (one pair) = __________

Question 40

A single card is selected from an ordinary deck of cards. The sample space is shown in the figure below. Find the probability P(heart and a jack). Give your answer as a fraction.

Question 41

Suppose a restaurant offers the following prix fixe menu: How many different dinners can this restaurant serve?

A)
B)
C)
D)
E)

Question 42

If a state issued license plates using the scheme of two letters followed by five digits, how many plates could it issue?

A) plates
B) plates
C) plates
D) plates
E) plates

Question 43

How many shirt-blouse outfits can a woman wear if she has 5 skirts and 6 blouses?

A) outfits
B) outfits
C) outfits
D) outfits
E) outfits

Question 44

Complete the list.

A)
B) 0
C) 1
D)
E)

Question 45

Find if .

A)
B)
C)
D)
E)

Question 46

A state issued license plates using the scheme of two letters followed by five digits, and 241 letter arrangements were not allowed. How many plates could it issue?

A) plates
B) plates
C) plates
D) plates
E) plates

Question 47

In your mathematics class, there are 28 students who attended class on the first day of the semester. 19 of the students brought a calculator to class that first day. If a student is randomly selected, what is the probability that student brought a calculator the first day?

Question 48

What is the probability of obtaining at least one head in 3 flips of a coin?

A)
B)
C)
D)
E)

Question 49

Find if .

A)
B)
C)
D)
E)

Question 50

Use estimation to select the best response. Do not calculate. Which of the following is less probable?

A) Obtaining a five at least 2 times in 3 rolls of a die
B) Obtaining a five 2 times in 3 rolls of a die
C) They are equally probable

Question 51

Complete the list.

A)
B)
C)
D)
E)

Question 52

A history teacher gives an 10-question true-false exam. In how many different ways can the test be answered, if the possible answers are true or false?

A)
B)
C)
D)
E)

Question 53

Find if .

A)
B)
C)
D)
E)

Question 54

Find if .

A)
B)
C)
D)
E)

Question 55

Complete the list.

A)
B)
C)
D)
E)

Question 56

In your mathematics class, there are 12 male and 17 female students who attended class on the first day of the semester. If you randomly select a student the first day, what is the probability you selected a female?

Question 57

What is the probability of obtaining a sum of at least 6 when rolling a pair of dice?

A)
B)
C)
D)
E)

Question 58

Use estimation to select the best response. Do not calculate. Which of the following is more probable?

A) Obtaining at least 2 heads in 3 flips of a coin
B) Obtaining at least 2 heads in 4 flips of a coin
C) They are equally probable

Question 59

Use estimation to select the best response. Do not calculate. Which of the following is less probable?

A) Guessing all the correct answers on a 20-question true-false examination
B) Obtaining all tails in 20 tosses of a penny
C) They are equally probable

Question 60

In your mathematics class, there are 28 students who attended class on the first day of the semester. 19 of the students brought a calculator to class that first day. If a student is randomly selected, what is the probability that student did not bring a calculator the first day?

Question 61

What is the probability of obtaining at least one tail in 4 flips of a coin? Give your answer as a fraction.

Question 62

How many shirt-blouse outfits can a woman wear if she has 4 skirts and 5 blouses?
__________ outfits

Question 63

Use estimation to select the best response. Do not calculate.
Which of the following is less probable?
Guessing all the incorrect answers on a 20-question true-false examination or
Obtaining all tails in 20 tosses of a quarter or
They are equally probable

Question 64

Complete the list.

Question 65

Find if . = __________

Question 66

Find if . = __________

Question 67

What is the probability of flipping a coin 8 times and obtaining all heads?

A)
B)
C)
D)
E)

Question 68

A state issued license plates using the scheme of two letters followed by three numerals. How many plates could it issue?
__________ plates

Question 69

Complete the list. Give your answer as a fraction.

Question 70

Find the probability of if . Give your answer as a fraction.

Question 71

Use estimation to select the best response. Do not calculate.
Which of the following is more probable?
Obtaining at least 3 heads in 5 flips of a coin or
Obtaining at least 3 heads in 6 flips of a coin or
They are equally probable

Question 72

Suppose a restaurant offers the following prix fixe menu:
How many different dinners can this restaurant serve? __________ different dinners

Question 73

A history teacher gives a 14-question true-false exam. In how many different ways can the test be answered if the possible answers are true or false?
__________ different ways

Question 74

What is the probability of a family with 6 children having 3 boys and 3 girls?

A)
B)
C)
D)
E)

Question 75

Find if = __________

Question 76

Use estimation to select the best response. Do not calculate.
Which of the following is more probable?
Obtaining a six 3 times in 5 rolls of a die or
Obtaining a six at least 3 times in 5 rolls of a die or
They are equally probable

Question 77

Complete the list.

Question 78

A typical Social Security identification number is 747-61-2313. How many Social Security numbers are possible if the first digit cannot be 0?
__________ numbers

Question 79

A state issued license plates using the scheme of three letters followed by three numerals, and 243 letter arrangements were not allowed. How many plates could it issue?
__________ plates

Question 80

A typical Social Security identification number is 805-83-3253. How many Social Security numbers are possible if the first digit of each group cannot be 0?

A)
B)
C)
D)
E)