Question 1

If P(A | B) = .3 and P(B) = .8, then _____.

Accepted Answer

A)  P(
A)  = .24 
B)  P(B | 
A)  = .7 
C)  P(A ∩ 
B)  = .5 
D)  P(A ∩ 
B)  = .24 
A)  P(
A)  = .24 
B)  P(B | 
A)  = .7 
C)  P(A ∩ 
B)  = .5 
D)  P(A ∩ 
B)  = .24 D

Question 2

You roll a fair six-sided die with the hopes of rolling a 5 or a 6. These two events are ___________ because they have no sample points in common.

Accepted Answer

A)  independent events 
B)  posterior events 
C)  mutually exclusive events 
D)  complements 
A)  independent events 
B)  posterior events 
C)  mutually exclusive events 
D)  complements C

Question 3

If a fair penny is tossed four times and comes up heads all four times, the probability of heads on the fifth trial is _____.

Accepted Answer

A)  0 
B)  1/32 
C)  1/2 
D)  1/5 
A)  0 
B)  1/32 
C)  1/2 
D)  1/5 C

Question 4

An experiment consists of three steps. There are four possible results on the first step, three possible results on the second step, and two possible results on the third step. The total number of experimental outcomes is _____.

Accepted Answer

A)  9 
B)  14 
C)  24 
D)  36 
A)  9 
B)  14 
C)  24 
D)  36

Question 5

If P(A) = .85, P(B) = .76, and P(A ? B) = .72, then P(A | B) = _____.

Accepted Answer

A)  .15 
B)  .53 
C)  .25 
D)  .95 
A)  .15 
B)  .53 
C)  .25 
D)  .95

Question 6

A sample point refers to a(n) _____.

Accepted Answer

A)  numerical measure of the likelihood of the occurrence of an event 
B)  set of all possible experimental outcomes 
C)  individual outcome of an experiment 
D)  All of the answers are correct. 
A)  numerical measure of the likelihood of the occurrence of an event 
B)  set of all possible experimental outcomes 
C)  individual outcome of an experiment 
D)  All of the answers are correct.

Question 7

Two events are mutually exclusive if _____.

Accepted Answer

A)  the probability of their intersection is 1 
B)  they have no sample points in common 
C)  the probability of their intersection is .5 
D)  the probability of their intersection is 1 and they have no sample points in common 
A)  the probability of their intersection is 1 
B)  they have no sample points in common 
C)  the probability of their intersection is .5 
D)  the probability of their intersection is 1 and they have no sample points in common

Question 8

The symbol ∩ shows the _____.

Accepted Answer

A)  union of events 
B)  intersection of events 
C)  sum of the probabilities of events 
D)  None of the answers is correct. 
A)  union of events 
B)  intersection of events 
C)  sum of the probabilities of events 
D)  None of the answers is correct.

Question 9

If A and B are mutually exclusive events with P(A) = .3 and P(B) = 0.5, then P(A ∩ B) =

Accepted Answer

A)  .30 
B)  .15 
C)  0 
D)  .20 
A)  .30 
B)  .15 
C)  0 
D)  .20

Question 10

If A and B are independent events with P(A) = .2 and P(B) = .6, then P(A ∪ B) = _____.

Accepted Answer

A)  .62 
B)  .12 
C)  .60 
D)  .68 
A)  .62 
B)  .12 
C)  .60 
D)  .68

Question 11

The multiplication law is potentially helpful when we are interested in computing the probability of _____.

Accepted Answer

A)  mutually exclusive events 
B)  the intersection of two events 
C)  the union of two events 
D)  None of the answers is correct. 
A)  mutually exclusive events 
B)  the intersection of two events 
C)  the union of two events 
D)  None of the answers is correct.

Question 12

A lottery is conducted using three urns. Each urn contains chips numbered from 0 to 9. One chip is selected at random from each urn. The total number of sample points in the sample space is _____.

Accepted Answer

A)  30 
B)  100 
C)  729 
D)  1,000 
A)  30 
B)  100 
C)  729 
D)  1,000

Question 13

Events A and B are mutually exclusive with P(A) = .3 and P(B) = .2. The probability of the complement of event B equals _____.

Accepted Answer

A)  0 
B)  .06 
C)  .70 
D)  None of the answers is correct. 
A)  0 
B)  .06 
C)  .70 
D)  None of the answers is correct.

Question 14

One of the basic requirements of probability is _____.

Accepted Answer

A)  for each experimental outcome Ei, we must have P(Ei) ≥ 1 
B)  P(
A)  = P(Ac) - 1 
C)  if there are k experimental outcomes, then P(E1) + P(E2) + ... + P(Ek) = 1 
D)  both P(
A)  = P(Ac) − 1 and if there are k experimental outcomes, then P(E1) + P(E2) + ... + P(Ek) = 1 
A)  for each experimental outcome Ei, we must have P(Ei) ≥ 1 
B)  P(
A)  = P(Ac) - 1 
C)  if there are k experimental outcomes, then P(E1) + P(E2) + ... + P(Ek) = 1 
D)  both P(
A)  = P(Ac) − 1 and if there are k experimental outcomes, then P(E1) + P(E2) + ... + P(Ek) = 1

Question 15

If A and B are mutually exclusive, then _____.

Accepted Answer

A)  P(
A)  + P(
B)  = 0 
B)  P(
A)  + P(
B)  = 1 
C)  P(A ⋂ 
B)  = 0 
D)  P(A ⋂ 
B)  = 1 
A)  P(
A)  + P(
B)  = 0 
B)  P(
A)  + P(
B)  = 1 
C)  P(A ⋂ 
B)  = 0 
D)  P(A ⋂ 
B)  = 1

Question 16

The symbol ∪ indicates the _____.

Accepted Answer

A)  union of events 
B)  intersection of events 
C)  sum of the probabilities of events 
D)  sample space 
A)  union of events 
B)  intersection of events 
C)  sum of the probabilities of events 
D)  sample space

Question 17

In an experiment, events A and B are mutually exclusive. If P(A) = .6, then the probability of B _____.

Accepted Answer

A)  cannot be larger than .4 
B)  can be any value greater than .6 
C)  can be any value between 0 and 1 
D)  cannot be determined with the information given 
A)  cannot be larger than .4 
B)  can be any value greater than .6 
C)  can be any value between 0 and 1 
D)  cannot be determined with the information given

Question 18

A __________ is a graphical representation in which the sample space is represented by a rectangle and events are represented as circles.

Accepted Answer

A)  frequency polygon 
B)  histogram 
C)  Venn diagram 
D)  tree diagram 
A)  frequency polygon 
B)  histogram 
C)  Venn diagram 
D)  tree diagram

Question 19

An experiment consists of tossing four coins successively. The number of sample points in this experiment is _____.

Accepted Answer

A)  16 
B)  8 
C)  4 
D)  2 
A)  16 
B)  8 
C)  4 
D)  2

Question 20

An experiment consists of four outcomes with P(E1) = .2, P(E2) = .3, and P(E3) = .4. The probability of outcome E4 is _____.

Accepted Answer

A)  .500 
B)  .024 
C)  .100 
D)  .900 
A)  .500 
B)  .024 
C)  .100 
D)  .900

Exam 4: Introduction to Probability

If P(A | B) = .3 and P(B) = .8, then _____.

You roll a fair six-sided die with the hopes of rolling a 5 or a 6. These two events are ___________ because they have no sample points in common.

If a fair penny is tossed four times and comes up heads all four times, the probability of heads on the fifth trial is _____.

An experiment consists of three steps. There are four possible results on the first step, three possible results on the second step, and two possible results on the third step. The total number of experimental outcomes is _____.

If P(A) = .85, P(B) = .76, and P(A ? B) = .72, then P(A | B) = _____.

A sample point refers to a(n) _____.

Two events are mutually exclusive if _____.

The symbol ∩ shows the _____.

If A and B are mutually exclusive events with P(A) = .3 and P(B) = 0.5, then P(A ∩ B) =

If A and B are independent events with P(A) = .2 and P(B) = .6, then P(A ∪ B) = _____.

The multiplication law is potentially helpful when we are interested in computing the probability of _____.

A lottery is conducted using three urns. Each urn contains chips numbered from 0 to 9. One chip is selected at random from each urn. The total number of sample points in the sample space is _____.

Events A and B are mutually exclusive with P(A) = .3 and P(B) = .2. The probability of the complement of event B equals _____.

One of the basic requirements of probability is _____.

If A and B are mutually exclusive, then _____.

The symbol ∪ indicates the _____.

In an experiment, events A and B are mutually exclusive. If P(A) = .6, then the probability of B _____.

A __________ is a graphical representation in which the sample space is represented by a rectangle and events are represented as circles.

An experiment consists of tossing four coins successively. The number of sample points in this experiment is _____.

An experiment consists of four outcomes with P(E1) = .2, P(E2) = .3, and P(E3) = .4. The probability of outcome E4 is _____.

Data and Statistics

Descriptive Statistics: Tabular and Graphical Displays

Descriptive Statistics: Numerical Measures

Discrete Probability Distributions

Continuous Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Tests

Inference About Means and Proportions With Two Populations

Inferences About Population Variances

Tests of Goodness of Fit, Independence, and Multiple Proportions

Experimental Design and Analysis of Variance

Simple Linear Regression

Multiple Regression

Regression Analysis: Model Building

Time Series Analysis and Forecasting

Nonparametric Methods

Statistical Methods for Quality Control

Decision Analysis

Sample Survey

Filters

An experiment consists of four outcomes with P(E₁) = .2, P(E₂) = .3, and P(E₃) = .4. The probability of outcome E₄ is _____.