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Question : Find the expected value of the random variable in the experiment : 2151705

**MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.**

**Find the expected value of the random variable in the experiment.**

1) Three coins are tossed, and the number of tails is noted.

A) 1

B) 1.75

C) 2

D) 1.5

2) Three cards are drawn from a deck without replacement. The number of aces is counted.

A) 1.0134

B) 0.2174

C) 1

D) 0.2308

3) A bag contains six marbles, of which four are red and two are blue. Suppose two marbles are chosen at random and X represents the number of red marbles in the sample.

A) 1.33

B) 1.4

C) 1

D) 0.933

4) Five rats are inoculated against a disease. The number contracting the disease is noted and the experiment is repeated 20 times. Find the probability distribution and the expected number of rats contracting the disease.

Total: overbar(20)

A) 2.3

B) 2.4

C) 0.9

D) 1

**Solve the problem.**

5) If 5 apples in a barrel of 25 apples are rotten, what is the expected number of rotten apples in a sample of 2 apples?

A) 0.63

B) 0.33

C) 1

D) 0.4

6) From a group of 3 men and 4 women, a delegation of 2 is selected. What is the expected number of men in the delegation?

A) 0.57

B) 1

C) 0.48

D) 0.86

7) If 3 balls are drawn from a bag containing 3 red and 4 blue balls, what is the expected number of red balls in the sample?

A) 1.29

B) 0.89

C) 1.54

D) 1.39

8) A contractor is considering a sale that promises a profit of $23,000 with a probability of 0.7 or a loss (due to bad weather, strikes, and such) of $9000 with a probability of 0.3. What is the expected profit?

A) $16,100

B) $13,400

C) $14,000

D) $22,400

9) Experience shows that a ski lodge will be full (158 guests) if there is a heavy snow fall in December, while only partially full (79 guests) with a light snow fall. What is the expected number of guests if the probability for a heavy snow fall is 0.40?

A) 126.4

B) 94.8

C) 110.6

D) 63.2

10) An insurance company has written 83 policies of $50,000, 485 of $25,000, and 902 of $10,000 on people of age 20. If the probability that a person will die at age 20 is 0.001, how much can the company expect to pay during the year the policies were written?

A) $2530

B) $252,950

C) $0

D) $25,295

11) An insurance company says that at age 50 one must choose to take $10,000 at age 60, $30,000 at 70, or $50,000 at 80 ($0 death benefit). The probability of living from 50 to 60 is 0.89, from 50 to 70, 0.66, and from 50 to 80, 0.48. Find the expected value at each age.

A) 60 - $6600

70 - $19,800

80 - $24,000

B) 60 - $8900

70 - $26,700

80 - $44,500

C) 60 - $8900

70 - $14,400

80 - $24,000

D) 60 - $8900

70 - $19,800

80 - $24,000

12) At age 50, Ann must choose between taking $18,000 at age 60 if she is alive then, or $32,000 at age 70 if she is alive then. The probability for a person aged 50 living to be 60 and 70 is 0.81 and 0.59, respectively. Using expected value, what is Ann's best option?

A) $18,000 at age 60

B) $32,000 at age 70

13) Find the expected number of boys in a family of 6 children.

A) 3.75

B) 4

C) 3.5

D) 3

14) Find the expected number of girls in a family of 3 children.

A) 2.25

B) 1.5

C) 2.5

D) 2

15) Find the expected number of girls in a family of 6.

A) 2.5

B) 3.5

C) 2.75

D) 3

16) If 2 cards are drawn from a deck of 52 cards, what is the expected number of spades?

A) 0.47

B) 0.25

C) 0.50

D) 0.75

17) Suppose you buy 1 ticket for $1 out of a lottery of 1000 tickets where the prize for the one winning ticket is to be $500. What is your expected payback?

A) -$0.50

B) $0

C) -$0.40

D) -$1.00

18) Suppose you pay $1.00 to roll a fair die with the understanding that you will get back $3.00 for rolling 3 or 5. What is your expected payback?

A) $0

B) -$2.00

C) $3.00

D) $1.00

19) Suppose a charitable organization decides to raise money by raffling a trip worth $500. If 3000 tickets are sold at $1.00 each, find the expected payback for a person who buys 1 ticket.

A) -$1.00

B) -$0.83

C) -$0.85

D) -$0.81

20) Numbers is a game where you bet $1.00 on any three-digit number from 000 to 999. If your number comes up, you get $600.00. Find the expected payback.

A) -$0.40

B) -$0.42

C) -$1.00

D) -$0.50

**Provide an appropriate response.**

21) Consider the selection of a nominating committee for a club. Is this a combination, a permutation, or neither?

A) Permutation

B) Combination

C) Neither

22) Consider the selection of officers for a club. Is this a combination, a permutation, or neither?

A) Permutation

B) Neither

C) Combination

23) Consider determining how many possible phone numbers are in an area code (repeated numbers allowe

D). Is this a combination, a permutation, or neither?

A) Combination

B) Permutation

C) Neither

**SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.**

27) Discuss the differences, both in applications and in the formulas, for combinations and permutations. Give an example of each.

28) Suppose that a class of 30 students is assigned to write an essay.

1) Suppose 4 essays are randomly chosen to appear on the class bulletin board. How many different groups of 4 are possible?

2) Suppose 4 essays are randomly chosen for awards of $10, $7, $5, and $3. How many different groups of 4 are possible?

Explain the significant differences between problems 1 and 2.

29) List the two requirements for a probability distribution. Discuss the relationship between the sum of the probabilities in a probability distribution and the total area represented by the bars in a probability histogram.

30) List the requirements for a binomial experiment. Describe an experiment which is binomial and explain how the experiment satisfies the requirements.