Question

1. A mutual fund company offers its customers a variety of funds: a money-market fund, three different bond funds (short, intermediate, and long-term), two stock funds (moderate and high-risk), and a balanced fund. Among customers who own shares in just one fund, the percentages of customers in the different funds are as follows. Money-market 25% High-risk stock 16% Short bond 10% Moderate-risk stock 25% Intermediate bond 8% Balanced 11% Long bond 5% A customer who owns shares in just one fund is randomly selected.

(a) What is the probability that the selected individual owns shares in the balanced fund? (

b) What is the probability that the individual owns shares in a bond fund?

(c) What is the probability that the selected individual does not own shares in a stock fund?

2. Suppose that 50% of all adults regularly consume coffee, 60% regularly consume carbonated soda, and 70% regularly consume at least one of these two products.

(a) What is the probability that a randomly selected adult regularly consumes both coffee and soda?
(b) What is the probability that a randomly selected adult doesn't regularly consume at least one of these two products?

3. Eighty percent of the light aircraft that disappear while in flight in a certain country are subsequently discovered. Of the aircraft that are discovered, 61% have an emergency locator, whereas 86% of the aircraft not discovered do not have such a locator. Suppose a light aircraft has disappeared. (Round your answers to three decimal places.)

(a) If it has an emergency locator, what is the probability that it will not be discovered?

(b) If it does not have an emergency locator, what is the probability that it will be discovered?

4. Suppose that the proportions of blood phenotypes in a particular population are as follows:

A	B	AB	O
0.50	0.07	0.04	0.39

a. Assuming that the phenotypes of two randomly selected individuals are independent of one another, what is the probability that both phenotypes are O? (Enter your answer to four decimal places.)


b. What is the probability that the phenotypes of two randomly selected individuals match? (Enter your answer to four decimal places.)

Answer 1

(a)

It is given that the 11% owns shares in the balanced fund so the probability the selected individual owns shares in the balanced fund is 0.11.

Answer: 0.11

(b)

There are three bond funds as follow:

Short bond 10%, Intermediate bond 8% , Long bond 5%

So the probability that the individual owns shares in a bond fund is

0.10 + 0.08 + 0.05 = 0.23

Answer: 0.23

(c)

There are two stock funds as follow:

High-risk stock 16%, Moderate-risk stock 25%

So the probability that the selected individual owns shares in a stock fund is

0.16 + 0.25 = 0.41

By the complement rule, the probability that the selected individual does not own shares in a stock fund is

1 - 0.41 = 0.59

Answer: 0.59

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2:

Let C shows the event that adult consume coffee and S shows the event that adult consume carbonated soda. So

(a)

By the addition rule of probability, the probability that a randomly selected adult regularly consumes both coffee and soda is,

(b)

By the complement rule, the probability that a randomly selected adult doesn't regularly consume at least one of these two products is,