Question 1

Suppose you randomly choose two cards from a thoroughly shuffled deck. If you put the first card back in the deck before you draw the second, what is the probability that the first card is an ace and the second card is a king?

Accepted Answer

A) 2/13 
B) 1/169 
C) 1/221 
D) 3/676

Question 2

You roll a die twice. The event of getting an even number on the first roll and another event of getting an odd number on the second roll are independent.

Accepted Answer

A) True 
 B)False

Question 3

What is your expected value of winning for a game whose probabilities and outcomes are given in the following table? Assume the wager is $1.

Accepted Answer

A) $1.30 
B) -$1.30 
C) $0.10 
D) -$0.10

Question 4

A teacher keeps track of the number of absences in a class each day along with their probabilities. Her results are in this table:  What is the expected number of absences for any given day?

Accepted Answer

A) 1.8 
B) 2.3 
C) 3.2 
D) 3.8

Question 5

You toss a coin and then roll a die. What is the probability that you get a head followed by a 4?

Accepted Answer

A) 1/4 
B) 5/12 
C) 1/12 
D) 1/2

Question 6

A _____ of a group of items is a selection from that group in which order is not taken into account.

Accepted Answer

A) combination 
B) listing 
C) permutation 
D) sequence

Question 7

A friend claims that it will rain today with probability 30% and tomorrow with probability four times as great as today. Which of the following is CORRECT?

Accepted Answer

A) The claim can be true because it is more likely to rain tomorrow if we have rain today. 
B) The claim cannot be true because raining tomorrow is not guaranteed. 
C) The claim can be true because it is possible to have rain tomorrow. 
D) The claim cannot be true because any probability is between 0 and 1.

Question 8

Suppose you toss a pair of dice. What is the probability that the total number of dots appearing is 6?

Accepted Answer

A) 5/6 
B) 5/36 
C) 1/6 
D) 25/36

Question 9

We have a box with six green marbles, five blue marbles, and seven red marbles. We choose three marbles from the box at random without looking. What is the probability that none of them will be blue?

Accepted Answer

A) 0.38 
B) 0.29 
C) 0.45 
D) 0.35

Question 10

A game is said to be fair if the expected value is:

Accepted Answer

A) positive. 
B) negative. 
C) large. 
D) zero.

Question 11

Suppose there is a group of nine people from whom we will make a committee. In how many ways could a four-person committee be selected?

Accepted Answer

A) 3024 
B) 36 
C) 24 
D) 126

Question 12

ABC College is using a new screening test to test its employees for TB. The following table shows the results of a pilot study:  For what percentage of the individuals in the study did the test return an INCORRECT result?

Accepted Answer

A) 89.1% 
B) 34.0% 
C) 15.8% 
D) 10.8%

Question 13

Each question on a multiple-choice exam has four choices. One of the choices is correct, worth four points. Another choice is wrong but carries partial credit of one point. The other two choices are wrong and worth negative one point. If a student picks answers at random, what is the expected value of his or her score for a problem?

Accepted Answer

A) 0.25 
B) 1.25 
C) 0.75 
D) 1.50

Question 14

The _____ of a test is the probability that the test will give a negative result for a person who does not have the disease.

Accepted Answer

A) specificity 
B) sensitivity 
C) false positive 
D) true negative

Question 15

If an experiment has only two unique possible outcomes, then the probability of getting one of those two outcomes is 0.5.

Accepted Answer

A) True 
 B)False

Question 16

Michael and Surrey are planning to have three children. Assuming it is equally likely for a boy or a girl to be born, what is the probability that at least one of their children will be a boy?

Accepted Answer

A) 1/8 
B) 3/8 
C) 5/8 
D) 7/8

Question 17

The probability of passing Professor Avila's math class is 65%, the probability of passing Professor Reid's biology class is 45%, and the probability of passing both is 25%. What is the probability of passing one or the other?

Accepted Answer

A) 75% 
B) 85% 
C) 70% 
D) 110%

Question 18

The following table gives the results of a screening test for a disease:  Estimate the sensitivity of the test.

Accepted Answer

A) 18.5% 
B) 80.6% 
C) 23.7% 
D) 53.3%

Question 19

A shoe store sells one brand of shoe in five styles, six sizes, and three colors. How many different types of shoes are available?

Accepted Answer

A) 33 
B) 90 
C) 14 
D) 150

Question 20

In a dice game, you win if the two dice come up 10 or higher. Otherwise, you lose $1. What should be the profit for winning to make this game fair?

Accepted Answer

A) $4 
B) $5 
C) $6 
D) $7

Exam 5: Introduction to Probability