Question 1

Determine whether the events A and B are independent.
-12 jurors are selected from a pool of 20 Event 
A: The first person selected is a woman
Event 
B: The second person selected is a woman

Accepted Answer

A) True 
 B)False

Question 2

Find the expected value.
-You are given 9 to 1 odds against rolling a sum of 8 with the roll of two fair dice, meaning you win $9 if you succeed and you lose $1 if you fail. Find the expected value (to you)of the game.

Accepted Answer

A) $0 
B) $1.25 
C) $0.39 
D) $0.09

Question 3

Find the indicated probability.
-Three coins are tossed 80 times and the number of heads is recorded. The results are shown in the table below. $$\begin{array} { l | c c c c } 
\text { Outcome } & 0 \text { heads } & 1 \text { head } & 2 \text { heads } & 3 \text { heads } \
\hline \text { Frequency } & 27 & 9 & 11 & 33
\end{array}$$ Compute the empirical probability that at most two heads occur.

Accepted Answer

A)  $\frac { 3 } { 4 }$ 
B)  $\frac { 47 } { 80 }$ 
C)  $\frac { 2 } { 9 }$ 
D)  10

Question 4

A knight may win a tournament. He may also fail to win the love of his lady. Are these events overlapping? Why or why not?

Accepted Answer

A) Yes, because some ladies love winners 
B) No, because not all ladies love all winners 
C) Yes, because not all ladies love all winners 
D) No, because all ladies love all winners

Question 5

Solve the problem.
-How many different three-number "combinations" are possible on a combination lock having 22 numbers on its dial? Assume that no numbers repeat. (Combination locks are really permutation
Locks.)

Accepted Answer

A)  9240 three-number "combinations" 
B)  $1.7556 \times 10 ^ { 5 }$ three-number "combinations" 
C)  $1.0534 \times 10 ^ { 6 }$ three-number "combinations" 
D)  $3.5112 \times 10 ^ { 5 }$ three-number "combinations"

Question 6

Make a probability distribution for the given set of events.
-When four fair coins are tossed, sixteen equally likely outcomes are possible as shown below: H?H? H?HT HHTH HHTT
HTHH HTHT HTTH HTTT
THHH THHT THTH THTT
TTHH TTHT TTTH TTTT Make a probability distribution for the number of tails when four fair coins are tossed.

Accepted Answer

A) 
$\begin{array}{r|r}
\text { Result } & \text { Probability } \
\hline 0 \mathrm{~T} & 1 / 16 \
1 \mathrm{~T} & 1 / 8 \
2 \mathrm{~T} & 3 / 8 \
3 \mathrm{~T} & 1 / 8 \
4 \mathrm{~T} & 1 / 16
\end{array}$ 
B) 
$\begin{array}{r|r}
\text { Result } & \text { Probability } \
\hline 0 \mathrm{~T} & 1 / 16 \
1 \mathrm{~T} & 3 / 16 \
2 \mathrm{~T} & 1 / 2 \
3 \mathrm{~T} & 3 / 16 \
4 \mathrm{~T} & 1 / 16
\end{array}$ 
C) 
$\begin{array}{r|r}
\text { Result } & \text { Probability } \
\hline 1 \mathrm{~T} & 1 / 4 \
2 \mathrm{~T} & 7 / 16 \
3 \mathrm{~T} & 1 / 4 \
4 \mathrm{~T} & 1 / 16
\end{array}$ 
D) 
$\begin{array}{r|r}
\text { Result } & \text { Probability } \
\hline 0 \mathrm{~T} & 1 / 16 \
1 \mathrm{~T} & 1 / 4 \
2 \mathrm{~T} & 3 / 8 \
3 \mathrm{~T} & 1 / 4 \
4 \mathrm{~T} & 1 / 16
\end{array}$

Question 7

A fair coin is tossed 5 times. Which of the following statements is (are)true? A: The sequence HTHTH is more likely than the sequence HHHHH.
B: The sequence HTHTH and the sequence HHHHH are equally likely.
C: Getting 5 tails is less likely than getting 3 tails.
D: Getting 5 tails and getting 3 tails are equally likely.

Accepted Answer

A)  $B$ and $C$ 
B)  $A$ and $C$ 
C)  $A$ and D 
D)  $B$ and $D$

Question 8

Solve the problem.
-A poker hand consists of 5 cards dealt from an ordinary deck of 52 playing cards. How many different hands are there consisting of four hearts and one spade?

Accepted Answer

A) 715 
B) 13 
C) 728 
D) 9295

Question 9

Evaluate the factorial expression.
-$\frac { 9 ! } { ( 9 - 6 ) ! }$

Accepted Answer

A)  504 
B)  9 
C)  60,480 
D)  1

Question 10

Find the expected value.
-A contractor is considering a sale that promises a profit of $39,000 with a probability of .7 or a loss (due to bad weather, strikes, and such)of $11,000 with a probability of .3. What is the expected
Profit?

Accepted Answer

A) $27,300 
B) $35,000 
C) $24,000 
D) $28,000

Question 11

Find the indicated probability. Round your answer to 6 decimal places when necessary.
-In January in a certain city the unconditional probability of rain on any given day of the month is 0.400. But the probability of rain on a day that follows a rainy day is 0.600 and the probability of
Rain on a day following a nonrainy day is 0.250. Find the probability of rain on three randomly
Selected consecutive days in January.

Accepted Answer

A) 0.144 
B) 0.090 
C) 0.064 
D) 0.216

Question 12

Solve the problem.
-Suppose a charitable organization decides to raise money by raffling a trip worth $500. If 3,000 tickets are sold at $1.00 each, find the expected net winnings for a person who buys 1 ticket.

Accepted Answer

A) -$0.85 
B) -$0.81 
C) -$1.00 
D) -$0.83

Question 13

Write the word or phrase that best completes each statement or answers the question.
-For a particular game at a casino, the expected winning for the player is -$0.87. How
would you interpret this statement?

Accepted Answer

The answer of Write the word or phrase that best...

Question 14

Write the word or phrase that best completes each statement or answers the question.
-Explain what is wrong with the statement below.
It's amazing that someone won the $100,000 prize in the lottery tonight. The probability of
winning $100,000 is only 0.000000512.

Accepted Answer

The answer of Write the word or phrase that best...

Question 15

Use the at least once rule to find the indicated probability.
-Find the probability of at least one club when you draw cards from a standard deck 17 times; assume that you replace the card each time you draw , so there are always 52 cards to draw from.

Accepted Answer

A) 0.003 
B) 0.744 
C) 0.992 
D) 0.008

Question 16

Find the expected value.
-Find the expected number of girls in a family of 7.

Accepted Answer

A) 4 
B) 3.25 
C) 3 
D) 3.5

Question 17

Write the word or phrase that best completes each statement or answers the question.
-A card is selected randomly from a standard deck of 52 cards. Let $\mathrm { A } = \text { event that the card is an ace. }$ Give examples of events B, C, and D such that A and B are independent, A and C are
dependent and overlapping, and A and D are non-overlapping.

Accepted Answer

The answer of Write the word or phrase that best...

Question 18

Solve the problem.
-A shoe store carries one brand of shoe in 5 different styles, 5 sizes, and 3 colors. How many different shoes are available of this one brand?

Accepted Answer

A) 125 
B) 75 
C) 13 
D) 30

Question 19

Find the expected value.
-In a game, you have a 1/43 probability of winning $82 and a 42/43 probability of losing $6. What is your expected winning?

Accepted Answer

A) $7.77 
B) $1.91 
C) -$3.95 
D) -$5.86

Question 20

Solve the problem.
-There are 5 members on a board of directors. If they must elect a chairperson, a secretary, and a treasurer, how many different slates of candidates are possible?

Accepted Answer

A) 125 
B) 10 
C) 120 
D) 60

Exam 7: Probability: Living With the Odds

Determine whether the events A and B are independent. -12 jurors are selected from a pool of 20 Event A: The first person selected is a woman Event B: The second person selected is a woman

Find the expected value. -You are given 9 to 1 odds against rolling a sum of 8 with the roll of two fair dice, meaning you win $9 if you succeed and you lose $1 if you fail. Find the expected value (to you) of the game.

A knight may win a tournament. He may also fail to win the love of his lady. Are these events overlapping? Why or why not?

Solve the problem. -How many different three-number "combinations" are possible on a combination lock having 22 numbers on its dial? Assume that no numbers repeat. (Combination locks are really permutation Locks.)

Solve the problem. -A poker hand consists of 5 cards dealt from an ordinary deck of 52 playing cards. How many different hands are there consisting of four hearts and one spade?

Evaluate the factorial expression. - $\frac { 9 ! } { ( 9 - 6 ) ! }$

Find the expected value. -A contractor is considering a sale that promises a profit of $39,000 with a probability of .7 or a loss (due to bad weather, strikes, and such) of $11,000 with a probability of .3. What is the expected Profit?

Solve the problem. -Suppose a charitable organization decides to raise money by raffling a trip worth $500. If 3,000 tickets are sold at $1.00 each, find the expected net winnings for a person who buys 1 ticket.

Write the word or phrase that best completes each statement or answers the question. -For a particular game at a casino, the expected winning for the player is -$0.87. How would you interpret this statement?

Write the word or phrase that best completes each statement or answers the question. -Explain what is wrong with the statement below. It's amazing that someone won the $100,000 prize in the lottery tonight. The probability of winning $100,000 is only 0.000000512.

Use the at least once rule to find the indicated probability. -Find the probability of at least one club when you draw cards from a standard deck 17 times; assume that you replace the card each time you draw , so there are always 52 cards to draw from.

Find the expected value. -Find the expected number of girls in a family of 7.

Solve the problem. -A shoe store carries one brand of shoe in 5 different styles, 5 sizes, and 3 colors. How many different shoes are available of this one brand?

Find the expected value. -In a game, you have a 1/43 probability of winning $82 and a 42/43 probability of losing $6. What is your expected winning?

Solve the problem. -There are 5 members on a board of directors. If they must elect a chairperson, a secretary, and a treasurer, how many different slates of candidates are possible?

Exam 7: Probability: Living With the Odds

Determine whether the events A and B are independent. -12 jurors are selected from a pool of 20 Event A: The first person selected is a woman Event B: The second person selected is a woman

Find the expected value. -You are given 9 to 1 odds against rolling a sum of 8 with the roll of two fair dice, meaning you win $9 if you succeed and you lose $1 if you fail. Find the expected value (to you) of the game.

A knight may win a tournament. He may also fail to win the love of his lady. Are these events overlapping? Why or why not?

Solve the problem. -How many different three-number "combinations" are possible on a combination lock having 22 numbers on its dial? Assume that no numbers repeat. (Combination locks are really permutation Locks.)

Solve the problem. -A poker hand consists of 5 cards dealt from an ordinary deck of 52 playing cards. How many different hands are there consisting of four hearts and one spade?

Evaluate the factorial expression. - 9!(9−6) !\frac { 9 ! } { ( 9 - 6 ) ! }(9−6) !9!​

Find the expected value. -A contractor is considering a sale that promises a profit of $39,000 with a probability of .7 or a loss (due to bad weather, strikes, and such) of $11,000 with a probability of .3. What is the expected Profit?

Solve the problem. -Suppose a charitable organization decides to raise money by raffling a trip worth $500. If 3,000 tickets are sold at $1.00 each, find the expected net winnings for a person who buys 1 ticket.

Write the word or phrase that best completes each statement or answers the question. -For a particular game at a casino, the expected winning for the player is -$0.87. How would you interpret this statement?

Write the word or phrase that best completes each statement or answers the question. -Explain what is wrong with the statement below. It's amazing that someone won the $100,000 prize in the lottery tonight. The probability of winning $100,000 is only 0.000000512.

Use the at least once rule to find the indicated probability. -Find the probability of at least one club when you draw cards from a standard deck 17 times; assume that you replace the card each time you draw , so there are always 52 cards to draw from.

Find the expected value. -Find the expected number of girls in a family of 7.

Solve the problem. -A shoe store carries one brand of shoe in 5 different styles, 5 sizes, and 3 colors. How many different shoes are available of this one brand?

Find the expected value. -In a game, you have a 1/43 probability of winning $82 and a 42/43 probability of losing $6. What is your expected winning?

Solve the problem. -There are 5 members on a board of directors. If they must elect a chairperson, a secretary, and a treasurer, how many different slates of candidates are possible?

Evaluate the factorial expression. - $\frac { 9 ! } { ( 9 - 6 ) ! }$