*Part I: Probability Problems*

**1**. A survey of subscribers to Forbes showed that 72% have investment in money
market funds (MMFs) and 36.4% have investments in certificates of deposit (CDs) ( Forbes
1993 Subscriber Study). If 20% have investments in both MMFs and CDs

Let MMFs denote the event that a randomly selected subscriber has investment in
money market funds - with P(MMFs) = .72.

Let CDs denote the event that a randomly selected subscriber has investment in
certificates of deposits - - with P(CDs) = .364

Let MMF and CDs denote the event that a randomly selected subscriber has
investment in both the money market funds and the CDs - with P(MMFs and CDs) =
.20

a) what is the probability that a subscriber has investments in either MMFs or CDs?

Ans: P(She/he holds either MMFs or CDs or both) = P(MMFs) + P(CDs) -
P(MMFs and CDs) = .__884__

b) what is the probability that a subscriber does not have investments in either MMFs or
CDs?

Ans: P(She/ he has **no** investment in either
MMFs or CDs) = 1- P(She/he does have ...) = 1 - .884 = __.116 __

2.** Text # 39, p. 148** **
**Ans:

a) A and B are not mutually exclusive events because there is not enough information to determine P(A and B).

b) B and C are mutually exclusive events assuming because both could not be determined as the primary cause of death since the occurrence of death by cancer precludes the occurrence of death by heart disease and vice versa. Thus P(B or C or Both) = P(B) + P(C) - P(B and C) = .25 + .20 - 0 =

c) Let C

*
Part I1: Expected Value problem*The corporate planning group of AB&C is considering two investment
alternatives for expanding its telephone service. Investment A limits its geographic
expansion to three big Midwest cities, while investment B covers five major cities on the
East Coast. The net profits for identical periods and probabilities of success for
investments A and B are given in the following table:

PROBABILITIES OF RETURN |
||

NET PROFITS (in $000) |
Investment A |
Investment B |

8,000 |
0.0 |
0.1 |

9,000 |
0.3 |
0.2 |

10,000 |
0.4 |
0.4 |

11,000 |
0.3 |
0.2 |

12,000 |
0.0 |
0.1 |

**a.)** Which investment option yields a higher expected return?

Ans: Let X denote the returns from investment option A

Let Y denote the returns from investment
option B

E(X) = $10,000 and E(Y) = $10,000
using the expected value formula. On the basis of the expected value, it is not clear which
option should be selected. The variance must thus be used to assess the risk
associated with each option in terms of the variability about the respective means of the two
investment options.

**
b.)** Compute the variance of each investment alternative. Can you make a decision on which

investment alternative is better, given this additional information?

Ans: Var(x) = 600,000 and Var(Y) = 1200,000. Thus, A is a
better option to select since the variability about the expected return of $10,000 is
smaller.

*
Part III: Binomial Distribution problem
*Text # 33, p. 196

**Part V: Normal Probability Distribution Problem
**

**
Part VI: Group Projects from the Manual: Use the Computer**

Ans: See your class notes

Exercise # 1.4, p. 44

Ans: See your class notes

Exercise # 1.6, p. 44

Ans: See your class notes

Exercise # 1, p. 48.

Ans:

Exercise # 2, p. 48.

Ans: See your class notes

Exercise # 4, p. 48

Ans: See your class notes

Exercise # 6, p. 48

Ans: See your class notes

**C: Normal Distribution Problems
**Exercise #2, p. 49

Ans: See your class notes

Exercise #4, p. 49

Ans: See your class notes

Exercise #5, p. 49

Ans:

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