Question 1

If a card is drawn from an ordinary deck of cards, and then a second card is
drawn from the same deck without replacing the first card, these two events are
.

Accepted Answer

The answer of If a card is drawn from an...

Question 2

What is the correct relationship between events A and B: A: Kathleen made an A on her Biology final exam.
B: Kathleen did not make an A on the Biology final exam.
A) A and B are mutually exclusive.
B) A and B are complementary.
C) A and B are not mutually exclusive.
D) If B is untrue, A is untrue.

Accepted Answer

The answer of What is the correct relationship between events...

Question 3

Let $A$ and $B$ be events with $P ( A ) = 0.2 , P ( B ) = 0.9$, and $P ( A$ and $B ) = 0.12$. Are $A$ and $B$ independent?
A) Yes
B) No

Accepted Answer

Two events $A$ and $B$ are independent if and only if $P(A \text{ and } B) = P(A)P(B)$. Here, $P(A)P(B) = 0.2 \times 0.9 = 0.18$, which is not equal to $P(A \text{ and } B) = 0.12$. Therefore, $A$ and $B$ are not independent.

Question 4

$$\text { If } P ( A ) = 0.38 , P ( B ) = 0.33 \text {, and } P ( A \text { and } B ) = 0.24 \text {, find } P ( A \text { or } B ) \text {. }$$
A) 0.47
B) 0.355
C) 0.12
D) 0.24

Accepted Answer

The probability of A or B occurring is given by P(A or B) = P(A) + P(B) - P(A and B) = 0.38 + 0.33 - 0.24 = 0.47.

Question 5

What is the correct relationship between events A and B: A: Laura participated in an out-of-town volleyball game at 11:00 AM last Friday.
B: Laura met with her academic advisor on campus at 11:00 AM last Friday.
A) A and B are mutually exclusive.
B) A and B are complementary.
C) A and B are not mutually exclusive.
D) If B is true, A is true.

Accepted Answer

Events A and B are mutually exclusive because Laura cannot be in two places at once, meaning she cannot participate in an out-of-town volleyball game and meet with her academic advisor on campus at the same time.

Question 6

Let $A$ and $B$ be events with $P ( A ) = 0.9 , P ( B ) = 0.8$, and $P ( A$ and $B ) = 0.36$. Are $A$ and $B$ mutually exclusive?
A) No
B) Yes

Accepted Answer

Events $A$ and $B$ are not mutually exclusive because $P(A \text{ and } B) = 0.36$ is greater than 0, indicating that there is an overlap between $A$ and $B$.

Question 7

What is the correct relationship between events A and B: A: Karl is college graduate.
B: Karl is a high school graduate.
A) A and B are mutually exclusive.
B) B is the complement of A.
C) A and B are not mutually exclusive.
D) If B is not true, A cannot be true.

Accepted Answer

A and B are not mutually exclusive because one can be both a college graduate and a high school graduate. Being a college graduate typically implies that one has also graduated from high school.

Question 8

Let $A$ and $B$ be events with $P ( A ) = 0.9 , P ( B ) = 0.4$, and $P ( A$ and $B ) = 0.36$. Are $A$ and $B$ independent?
A) Yes
B) No

Accepted Answer

The answer of Let $A$ and $B$ be events with...

Question 9

$$\text { Let } A \text { and } B \text { be events with } P ( A ) = 0.7 , P ( B ) = 0.3 \text {, and } P ( B \mid A ) = 0.2 \text {. Find } P ( A \text { and } B ) \text {. }$$
A) 0.29
B) 0.21
C) 0.14
D) 0.06

Accepted Answer

The probability of A and B occurring together, $P(A \text{ and } B)$, can be found using the formula for conditional probability: $P(A \text{ and } B) = P(B|A) \times P(A)$. Substituting the given values, we get $0.2 \times 0.7 = 0.14$.

Question 10

For the event described below, which of the following represents the complement of the event. A sample of 363 software DVDs was selected. At least 29 of these were defective.
A) Exactly 29 DVDs were not defective.
B) At most 29 DVDs were defective.
C) Fewer than 29 DVDs were defective.
D) At most 334 DVDs were not defective.

Accepted Answer

The complement of "at least 29 of these were defective" is "fewer than 29 DVDs were defective," because it represents all outcomes that are not included in the original event.

Question 11

$$\text { If } P ( A ) = 0.46 , P ( B ) = 0.5 \text {, and } A \text { and } B \text { are mutually exclusive, find } P ( A \text { or } B ) \text {. }$$
A) 0.04
B) 0.48
C) 0.96
D) 0

Accepted Answer

Since A and B are mutually exclusive, $ P(A \text{ or } B) = P(A) + P(B) = 0.46 + 0.5 = 0.96 $.

Question 12

Given the following Venn diagram, which of the following equations could be used to Calculate the probability of either event $ A $, event $ B $, or event $ C $ occurring.

A) 
B) 
C) 
D)

Accepted Answer

The answer of Given the following Venn diagram, which of...

Question 13

Let $A , B$ and $C$ be independent events with $P ( A ) = 0.1 , P ( B ) = 0.7$, and $P ( C ) = 0.9$. Find $P ( A$ and $B$ and $C )$.
A) 0.063
B) 0.078
C) 0.037
D) 0.07

Accepted Answer

Since $A$, $B$, and $C$ are independent events, the probability of all three occurring is the product of their individual probabilities: $P(A \text{ and } B \text{ and } C) = P(A) \times P(B) \times P(C) = 0.1 \times 0.7 \times 0.9 = 0.063.$

Question 14

A poll was taken of 13,863 working adults aged 40-70 to determine their level of educatic The participants were classified by sex and by level of education. The results were as folls
$\begin{array}{cccc}
\hline \text { Education Level } & \text { Male } & \text { Female } & \text { Total } \
\hline \text { High School or Less } & 3043 & 2133 & 5176 \
\text { Bachelor's Degree } & 3428 & 4150 & 7578 \
\text { Master's Degree } & 554 & 423 & 977 \
\text { Ph.D. } & 72 & 60 & 132 \
\hline \text { Total } & 7097 & 6766 & 13,863
\end{array}$
A person is selected at random. Compute the probability that the person is male or has a P .D.
A) 0.516
B) 0.512
C) 0.521
D) 0.010

Accepted Answer

The probability that the person is male or has a Ph.D. is calculated by adding the probability of being male to the probability of having a Ph.D., and then subtracting the probability of being both male and having a Ph.D. (to correct for double counting). The number of males is 7097, the total number of participants is 13863, and the total number of people with a Ph.D. is 132, with 72 being male. So, the calculation is $(7097 + 132 - 72) / 13863 = 7157 / 13863 \approx 0.516$.

Question 15

For the event described below, which of the following represents the complement of the event. A sample of 351 software DVDs was selected. Exactly 29 of these were defective.
A) Exactly 322 DVDs were not defective.
B) No more than 29 DVDs were defective.
C) Exactly 29 DVDs were not defective.
D) The number of defective DVDs was not equal to 29.

Accepted Answer

The complement of the event "Exactly 29 of these were defective" is "The number of defective DVDs was not equal to 29."

Question 16

$$\text { If } P ( A ) = 0.35 , P ( B ) = 0.85 \text {, and } P ( A \text { or } B ) = 0.86 \text {, are } A \text { and } B \text { mutually exclusive? }$$
A) No
B) Yes

Accepted Answer

Events A and B are not mutually exclusive because P(A or B) is not equal to the sum of P(A) + P(B), which would be 1.2, indicating some overlap. Since P(A or B) is less than this sum, it means A and B have some common outcomes.

Question 17

For the event described below, which of the following represents the complement of the event. A sample of 318 software DVDs was selected. Fewer than 44 of these were
Defective.
A) At most 44 DVDs were not defective.
B) At least 44 DVDs were defective.
C) More than 44 DVDs were not defective.
D) Fewer than 44 DVDs were not defective.

Accepted Answer

The complement of "fewer than 44 DVDs were defective" is "at least 44 DVDs were defective," meaning 44 or more DVDs were defective. This is because the complement of an event includes all outcomes that are not in the original event.

Question 18

Let $A$ and $B$ be events with $P ( A ) = 0.5 , P ( B ) = 0.4$. Assume that $A$ and $B$ are independent. Find $P ( A$ and $B )$.
A) 0.8
B) 0.2
C) 0.5
D) 0.4

Accepted Answer

For independent events $A$ and $B$, $P(A \text{ and } B) = P(A) \times P(B) = 0.5 \times 0.4 = 0.2$.

Question 19

A poll was taken of 14,356 working adults aged 40-70 to determine their level of educatic The participants were classified by sex and by level of education. The results were as folls
$\begin{array}{cccc}
\hline \text { Education Level } & \text { Male } & \text { Female } & \text { Total } \
\hline \text { High School or Less } & 3396 & 2340 & 5736 \
\text { Bachelor's Degree } & 3466 & 4026 & 7492 \
\text { Master's Degree } & 522 & 478 & 1000 \
\text { Ph.D. } & 72 & 56 & 128 \
\hline \text { Total } & 7456 & 6900 & 14,356
\end{array}$
A person is selected at random. Compute the probability that the person has a master's des ee.
A) 0.035
B) 0.033
C) 0.036
D) 0.070

Accepted Answer

The answer of A poll was taken of 14,356 working...

Question 20

$$\text { If } P ( A ) = 0.45 , P ( B ) = 0.41 \text {, and } P ( A \text { or } B ) = 0.86 \text {, are } A \text { and } B \text { mutually exclusive? }$$
A) Yes
B) No

Accepted Answer

A and B are not mutually exclusive because P(A or B) = 0.86, which is greater than P(A) + P(B) = 0.45 + 0.41 = 0.86. This means that there is some overlap between events A and B, so they are not mutually exclusive.

Quiz 4: Probability and Counting Rules

If a card is drawn from an ordinary deck of cards, and then a second card is drawn from the same deck without replacing the first card, these two events are .

What is the correct relationship between events A and B: A: Kathleen made an A on her Biology final exam. B: Kathleen did not make an A on the Biology final exam.

Let $A$ and $B$ be events with $P ( A ) = 0.2 , P ( B ) = 0.9$ , and $P ( A$ and $B ) = 0.12$ . Are $A$ and $B$ independent?

$\text { If } P ( A ) = 0.38 , P ( B ) = 0.33 \text {, and } P ( A \text { and } B ) = 0.24 \text {, find } P ( A \text { or } B ) \text {. }$

What is the correct relationship between events A and B: A: Laura participated in an out-of-town volleyball game at 11:00 AM last Friday. B: Laura met with her academic advisor on campus at 11:00 AM last Friday.

Let $A$ and $B$ be events with $P ( A ) = 0.9 , P ( B ) = 0.8$ , and $P ( A$ and $B ) = 0.36$ . Are $A$ and $B$ mutually exclusive?

What is the correct relationship between events A and B: A: Karl is college graduate. B: Karl is a high school graduate.

Let $A$ and $B$ be events with $P ( A ) = 0.9 , P ( B ) = 0.4$ , and $P ( A$ and $B ) = 0.36$ . Are $A$ and $B$ independent?

$\text { Let } A \text { and } B \text { be events with } P ( A ) = 0.7 , P ( B ) = 0.3 \text {, and } P ( B \mid A ) = 0.2 \text {. Find } P ( A \text { and } B ) \text {. }$

For the event described below, which of the following represents the complement of the event. A sample of 363 software DVDs was selected. At least 29 of these were defective.

$\text { If } P ( A ) = 0.46 , P ( B ) = 0.5 \text {, and } A \text { and } B \text { are mutually exclusive, find } P ( A \text { or } B ) \text {. }$

Given the following Venn diagram, which of the following equations could be used to Calculate the probability of either event $A$ , event $B$ , or event $C$ occurring.

Let $A , B$ and $C$ be independent events with $P ( A ) = 0.1 , P ( B ) = 0.7$ , and $P ( C ) = 0.9$ . Find $P ( A$ and $B$ and $C )$ .

For the event described below, which of the following represents the complement of the event. A sample of 351 software DVDs was selected. Exactly 29 of these were defective.

$\text { If } P ( A ) = 0.35 , P ( B ) = 0.85 \text {, and } P ( A \text { or } B ) = 0.86 \text {, are } A \text { and } B \text { mutually exclusive? }$

For the event described below, which of the following represents the complement of the event. A sample of 318 software DVDs was selected. Fewer than 44 of these were Defective.

Let $A$ and $B$ be events with $P ( A ) = 0.5 , P ( B ) = 0.4$ . Assume that $A$ and $B$ are independent. Find $P ( A$ and $B )$ .

$\text { If } P ( A ) = 0.45 , P ( B ) = 0.41 \text {, and } P ( A \text { or } B ) = 0.86 \text {, are } A \text { and } B \text { mutually exclusive? }$

Quiz 4: Probability and Counting Rules

If a card is drawn from an ordinary deck of cards, and then a second card is drawn from the same deck without replacing the first card, these two events are .

What is the correct relationship between events A and B: A: Kathleen made an A on her Biology final exam. B: Kathleen did not make an A on the Biology final exam.

Let AAA and BBB be events with P(A) =0.2,P(B) =0.9P ( A ) = 0.2 , P ( B ) = 0.9P(A) =0.2,P(B) =0.9 , and P(AP ( AP(A and B) =0.12B ) = 0.12B) =0.12 . Are AAA and BBB independent?

If P(A) =0.38,P(B) =0.33, and P(A and B) =0.24, find P(A or B) . \text { If } P ( A ) = 0.38 , P ( B ) = 0.33 \text {, and } P ( A \text { and } B ) = 0.24 \text {, find } P ( A \text { or } B ) \text {. } If P(A) =0.38,P(B) =0.33, and P(A and B) =0.24, find P(A or B) .