Question

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 10% Moderate-risk stock 15% Short bond 12% Intermediate bond 7% Long bond 8% Balanced 23% 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? For your answer, please report the answer in decimals. For example, 50% would be submitted as .5.

Answer 1

Part b and c are missing and they are;

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?

Answer:

A) P(balanced fund) = 0.23

B) P(bond fund) = 0.27

C) P(no stock fund) = 0.75

Explanation:

We are given the percentages of customers in the different funds as follows:

Money-market: 25%

High-risk stock: 10%

Moderate-risk stock: 15%

Short bond: 12%

Intermediate bond: 7%

Long bond: 8%

Balanced: 23%

A) From the percentages given, we can see that the balanced fund is 23%.

Thus,this represents the probability as addition of all the given percentages gives 100%

Thus, probability that the selected individual owns shares in the balanced fund is;

P(balanced fund) = 23% = 0.23

B) From the percentages given, bond funds given are;

Short bond: 12%

Intermediate bond: 7%

Long bond: 8%

Thus,

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

P(bond fund) = 12% + 7% + 8%

P(bond fund) = 27% = 0.27

C) Probability that the selected individual doesn't own shares in a stock fund is;

P(no stock fund) = 1 - P(stuck fund)

P(stuck fund) = High-risk stock +

Moderate-risk stock = 10% + 15% = 25% = 0.25

Thus;

P(no stock fund) = 1 - 0.25 = 0.75