Question 1

62) Let $A , B$ and $C$ be independent events with $P ( A ) = 0.6 , P ( B ) = 0.3$, and $P ( C ) = 0.2$. Find $P ( A$ and $B$ and $C$ ).

Accepted Answer

A)  $0.18$ 
B)  $0.036$ 
C)  $0.9$ 
D)  $0.033$ 
A)  $0.18$ 
B)  $0.036$ 
C)  $0.9$ 
D)  $0.033$

Question 2

For this year's mayoral election, voter dissatisfaction is very high. In a survey of 800 likely voters, 231 said they planned to write in an independent candidate rather than vote for the Democrat or Republican candidate for mayor. Estimate the percentage of voters who plan to write in an independent candidate?

Accepted Answer

A) 28.875% 
B) 71.125% 
C) 80% 
D) 23.1% 
A) 28.875% 
B) 71.125% 
C) 80% 
D) 23.1%

Question 3

If P(A) = 0.33, P(B) = 0.51, and A and B are mutually exclusive, find P(A or B).

Accepted Answer

A)   0.84 
B)  0 
C)   0.42 
D)   0.18 
A)   0.84 
B)  0 
C)   0.42 
D)   0.18

Question 4

Nanette must pass through three doors as she walks from her company's foyer to her office. Each of these doors may be locked or unlocked. Let B be the event that exactly two doors are locked. List the outcomes of B. [Let "L"
designate "locked" and U" designate "unlocked".]

Accepted Answer

A) {LLL, LLU, LUL, LUU, ULL, ULU, UUL, UUU} 
B) {LLU, LUL, ULL} 
C) {LLU, LUL, ULL, LUU, ULU, UUL} 
D) None of these. 
A) {LLL, LLU, LUL, LUU, ULL, ULU, UUL, UUU} 
B) {LLU, LUL, ULL} 
C) {LLU, LUL, ULL, LUU, ULU, UUL} 
D) None of these.

Question 5

A section of an exam contains two multiple-choice questions, each with three answer choices (listed "A", "B", and "C"). Assuming the outcomes to be equally likely, find the probability (as a reduced fraction) that both answers are "C". [Hint: List all the outcomes of the sample space first.]

Accepted Answer

A)  $1 / 3$ 
B)  $1 / 6$ 
C)  $1 / 9$ 
D)  $1 / 27$ 
A)  $1 / 3$ 
B)  $1 / 6$ 
C)  $1 / 9$ 
D)  $1 / 27$

Question 6

So far this season, the university's football team has executed 163 running plays, 138 passing plays, and 24 "trick" plays. What is the probability that the team will not execute a trick play?

Accepted Answer

A) 0.08 
B) 0.074 
C) 0.926 
D) 0.92 
A) 0.08 
B) 0.074 
C) 0.926 
D) 0.92

Question 7

Let E be the event that a corn crop has an infestation of ear worms, and let B be the event that a corn crop has an infestation of corn borers. Suppose that $P ( E ) = 0.23 , P ( B ) = 0.11$, and $P ( E$ and $B ) = 0.05$. Find the probability that a corn crop has no corn borer infestation.

Accepted Answer

A)  $0.77$ 
B)  $0.89$ 
C)  $0.66$ 
D)  $0.29$ 
A)  $0.77$ 
B)  $0.89$ 
C)  $0.66$ 
D)  $0.29$

Question 8

The numbers 1 through 10 are written in separate slips of paper, and the slips are placed into a box. Then, 4 of these slips are drawn at random.
What is the probability that the drawn slips are "1", "2", "3", and "4", in that order?

Accepted Answer

A) 0.00476 
B) 0.000198 
C) 0.004752 
D) 0.11424 
A) 0.00476 
B) 0.000198 
C) 0.004752 
D) 0.11424

Question 9

On a TV game show, a contestant is shown 10 products from a grocery store and is asked to choose the three least-expensive items in the set, and then correctly arrange these three items in order of price. In how many ways can the contestant choose the three items?

Accepted Answer

A) 6 
B) 720 
C) 604,800 
D) 120 
A) 6 
B) 720 
C) 604,800 
D) 120

Question 10

Assume a soldier is selected at random from the Army. Determine whether the events A and B are independent, mutually exclusive, or neither.
A: The soldier is a corporal.
B: The soldier is a colonel

Accepted Answer

A) mutually exclusive 
B) neither 
C) independent 
A) mutually exclusive 
B) neither 
C) independent

Question 11

A fair die is rolled five times. What is the probability that it comes up 5 at least once?

Accepted Answer

A) 0.1667 
B) 0.5981 
C) 0.5177 
D) 0.8333 
A) 0.1667 
B) 0.5981 
C) 0.5177 
D) 0.8333

Question 12

Nanette must pass through three doors as she walks from her company's foyer to her office. Each of these doors may be locked or unlocked. List the outcomes of the sample space

Accepted Answer

A) {LLU, LUL, ULL, UUL, ULL, LUU} 
B) {LLL, UUU} 
C) {LLL, LLU, LUL, LUU, ULL, ULU, UUL, UUU} 
D) None of these. 
A) {LLU, LUL, ULL, UUL, ULL, LUU} 
B) {LLL, UUU} 
C) {LLL, LLU, LUL, LUU, ULL, ULU, UUL, UUU} 
D) None of these.

Question 13

A section of an exam contains two multiple-choice questions, each with three answer choices (listed "A", "B", and "C"). Assuming the outcomes to be equally likely, find the probability (as a reduced fraction) that neither of the answers is "B". [Hint: List all the outcomes of the sample space first.]

Accepted Answer

A)  $4 / 9$ 
B)  $2 / 3$ 
C)  $5 / 9$ 
D)  $1 / 3$ 
A)  $4 / 9$ 
B)  $2 / 3$ 
C)  $5 / 9$ 
D)  $1 / 3$

Question 14

Let A and B be events with P(A) = 0.9, P(B) = 0.5, and P(A and B) = 0.45. Are A and B independent?

Accepted Answer

A) True 
 B)False

Question 15

A poll was taken of 14,972 working adults aged 40-70 to determine their level of education. The participants were classified by sex and by level of education. The results were as follows
$\begin{array} { c c c c } 
\hline \text { Education Level } & \text { Male } & \text { Female } & \text { Total } \
\hline \text { High School or Less } & 3594 & 2729 & 6323 \
\text { Bachelor's Degree } & 3245 & 3652 & 6897 \
\text { Master's Degree } & 566 & 401 & 967 \
\text { Ph.D. } & 63 & 42 & 105 \
\hline \text { Total } & 7468 & 6824 & 14,292
\end{array}$
A person is selected at random. Compute the probability that the person is female and has a bachelor's degree.

Accepted Answer

A) 0.229 
B) 0.538 
C) 0.963 
D) 0.257 
A) 0.229 
B) 0.538 
C) 0.963 
D) 0.257

Question 16

A fair coin is tossed four times. What is the probability that the sequence of tosses is HHTT?

Accepted Answer

A) 0.038 
B) 0.125 
C) 0.0625 
D) 0.25 
A) 0.038 
B) 0.125 
C) 0.0625 
D) 0.25

Question 17

In a recent semester at a local university, 520 students enrolled in both General Chemistry and Calculus I. Of these students, 88 received an A in general chemistry, 76 received an A in calculus, and 31 received an A in both general chemistry and calculus.
Find the probability that a randomly chosen student received an A in general chemistry or calculus or both.

Accepted Answer

A) 0.811 
B) 0.375 
C) 0.256 
D) 0.315 
A) 0.811 
B) 0.375 
C) 0.256 
D) 0.315

Question 18

A 12-sided die can be made from a geometric solid called a dodecahedron. Assume that a fair dodecahedron is rolled. The sample space is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Find P(Greater than 8).

Accepted Answer

A)  $7 / 12$ 
B)  $1 / 12$ 
C)  $1 / 3$ 
D)  $1 / 4$ 
A)  $7 / 12$ 
B)  $1 / 12$ 
C)  $1 / 3$ 
D)  $1 / 4$

Question 19

So far this season, the university's football team has executed 149 running plays, 157 passing plays, and 20 "trick" plays. What is the probability that the team will execute a passing play?

Accepted Answer

A) 0.513 
B) 0.457 
C) 0.482 
D) 0.518 
A) 0.513 
B) 0.457 
C) 0.482 
D) 0.518

Question 20

A poll was taken of 14,056 working adults aged 40-70 to determine their level of education. The participants were classified by sex and by level of education. The results were as follows.
 $\begin{array} { c c c c } 
\hline \text { Education Level } & \text { Male } & \text { Female } & \text { Total } \
\hline \text { High School or Less } & 3141 & 2434 & 5575 \
\text { Bachelor's Degree } & 3619 & 3761 & 7380 \
\text { Master's Degree } & 534 & 472 & 1006 \
\text { Ph.D. } & 52 & 43 & 95 \
\hline \text { Total } & 7346 & 6710 & 14,056
\end{array}$
A person is selected at random. Compute the probability that the person has a master's degree

Accepted Answer

A) 0.036 
B) 0.034 
C) 0.072 
D) 0.038 
A) 0.036 
B) 0.034 
C) 0.072 
D) 0.038

62) Let $A , B$ and $C$ be independent events with $P ( A ) = 0.6 , P ( B ) = 0.3$ , and $P ( C ) = 0.2$ . Find $P ( A$ and $B$ and $C$ ).

If P(A) = 0.33, P(B) = 0.51, and A and B are mutually exclusive, find P(A or B).

Nanette must pass through three doors as she walks from her company's foyer to her office. Each of these doors may be locked or unlocked. Let B be the event that exactly two doors are locked. List the outcomes of B. [Let "L" designate "locked" and U" designate "unlocked".]

A section of an exam contains two multiple-choice questions, each with three answer choices (listed "A", "B", and "C"). Assuming the outcomes to be equally likely, find the probability (as a reduced fraction) that both answers are "C". [Hint: List all the outcomes of the sample space first.]

So far this season, the university's football team has executed 163 running plays, 138 passing plays, and 24 "trick" plays. What is the probability that the team will not execute a trick play?

Let E be the event that a corn crop has an infestation of ear worms, and let B be the event that a corn crop has an infestation of corn borers. Suppose that $P ( E ) = 0.23 , P ( B ) = 0.11$ , and $P ( E$ and $B ) = 0.05$ . Find the probability that a corn crop has no corn borer infestation.

The numbers 1 through 10 are written in separate slips of paper, and the slips are placed into a box. Then, 4 of these slips are drawn at random. What is the probability that the drawn slips are "1", "2", "3", and "4", in that order?

On a TV game show, a contestant is shown 10 products from a grocery store and is asked to choose the three least-expensive items in the set, and then correctly arrange these three items in order of price. In how many ways can the contestant choose the three items?

Assume a soldier is selected at random from the Army. Determine whether the events A and B are independent, mutually exclusive, or neither. A: The soldier is a corporal. B: The soldier is a colonel

A fair die is rolled five times. What is the probability that it comes up 5 at least once?

Nanette must pass through three doors as she walks from her company's foyer to her office. Each of these doors may be locked or unlocked. List the outcomes of the sample space

Let A and B be events with P(A) = 0.9, P(B) = 0.5, and P(A and B) = 0.45. Are A and B independent?

A fair coin is tossed four times. What is the probability that the sequence of tosses is HHTT?

A 12-sided die can be made from a geometric solid called a dodecahedron. Assume that a fair dodecahedron is rolled. The sample space is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Find P(Greater than 8).

So far this season, the university's football team has executed 149 running plays, 157 passing plays, and 20 "trick" plays. What is the probability that the team will execute a passing play?

Basic Ideas

Graphical Summaries of Data

Numerical Summaries of Data

Probability

The Normal Distribution

Confidence Intervals

Hypothesis Testing

Inferences on Two Samples

Tests With Qualitative Data

Correlation and Regression

Statistical Analysis Questions in ANOVA and Rank-Sum Test

Filters

Exam 5: Discrete Probability Distributions

62) Let A,BA , BA,B and CCC be independent events with P(A)=0.6,P(B)=0.3P ( A ) = 0.6 , P ( B ) = 0.3P(A)=0.6,P(B)=0.3 , and P(C)=0.2P ( C ) = 0.2P(C)=0.2 . Find P(AP ( AP(A and BBB and CCC ).

If P(A) = 0.33, P(B) = 0.51, and A and B are mutually exclusive, find P(A or B).

Nanette must pass through three doors as she walks from her company's foyer to her office. Each of these doors may be locked or unlocked. Let B be the event that exactly two doors are locked. List the outcomes of B. [Let "L" designate "locked" and U" designate "unlocked".]

A section of an exam contains two multiple-choice questions, each with three answer choices (listed "A", "B", and "C"). Assuming the outcomes to be equally likely, find the probability (as a reduced fraction) that both answers are "C". [Hint: List all the outcomes of the sample space first.]

So far this season, the university's football team has executed 163 running plays, 138 passing plays, and 24 "trick" plays. What is the probability that the team will not execute a trick play?

The numbers 1 through 10 are written in separate slips of paper, and the slips are placed into a box. Then, 4 of these slips are drawn at random. What is the probability that the drawn slips are "1", "2", "3", and "4", in that order?

On a TV game show, a contestant is shown 10 products from a grocery store and is asked to choose the three least-expensive items in the set, and then correctly arrange these three items in order of price. In how many ways can the contestant choose the three items?

Assume a soldier is selected at random from the Army. Determine whether the events A and B are independent, mutually exclusive, or neither. A: The soldier is a corporal. B: The soldier is a colonel

A fair die is rolled five times. What is the probability that it comes up 5 at least once?

Nanette must pass through three doors as she walks from her company's foyer to her office. Each of these doors may be locked or unlocked. List the outcomes of the sample space

Let A and B be events with P(A) = 0.9, P(B) = 0.5, and P(A and B) = 0.45. Are A and B independent?

A fair coin is tossed four times. What is the probability that the sequence of tosses is HHTT?

A 12-sided die can be made from a geometric solid called a dodecahedron. Assume that a fair dodecahedron is rolled. The sample space is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Find P(Greater than 8).

So far this season, the university's football team has executed 149 running plays, 157 passing plays, and 20 "trick" plays. What is the probability that the team will execute a passing play?

Basic Ideas

Graphical Summaries of Data

Numerical Summaries of Data

Probability

The Normal Distribution

Confidence Intervals

Hypothesis Testing

Inferences on Two Samples

Tests With Qualitative Data

Correlation and Regression

Statistical Analysis Questions in ANOVA and Rank-Sum Test

Filters

62) Let $A , B$ and $C$ be independent events with $P ( A ) = 0.6 , P ( B ) = 0.3$ , and $P ( C ) = 0.2$ . Find $P ( A$ and $B$ and $C$ ).