1. A mutual fund company offers its clients several funds: a money market fund, three bond funds (short-term, intermediate-term, and long-term), two stock funds (moderate-risk and high-risk), and a balanced fund. The percentages of clients holding shares in a single fund are distributed among the different types of investment instruments as follows: PERCENTAGE TYPE Moderate risk stocks 25% Money market 20% High-risk stocks 18% Short-term bonds 15% Intermediate-term bonds 10% Balanced 7% Long-term bonds 5% TOTAL 100 % If a client is randomly selected who owns shares in only one fund: a) What is the probability that the selected client owns shares in the balanced fund? b) What is the probability that the same client owns shares in a bond fund? c) What is the probability that the same client does not own shares in a stock fund?

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Answer to a math question 1. A mutual fund company offers its clients several funds: a money market fund, three bond funds (short-term, intermediate-term, and long-term), two stock funds (moderate-risk and high-risk), and a balanced fund. The percentages of clients holding shares in a single fund are distributed among the different types of investment instruments as follows: PERCENTAGE TYPE Moderate risk stocks 25% Money market 20% High-risk stocks 18% Short-term bonds 15% Intermediate-term bonds 10% Balanced 7% Long-term bonds 5% TOTAL 100 % If a client is randomly selected who owns shares in only one fund: a) What is the probability that the selected client owns shares in the balanced fund? b) What is the probability that the same client owns shares in a bond fund? c) What is the probability that the same client does not own shares in a stock fund?

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Sigrid

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a) To find the probability that the selected client owns shares in the balanced fund:

P(\text{Balanced fund}) = \frac{\text{Percentage of clients in balanced fund}}{\text{Total percentage}} = \frac{7}{100} = 0.07

b) To find the probability that the same client owns shares in a bond fund:

P(\text{Bond fund}) = P(\text{Short-term}) + P(\text{Intermediate-term}) + P(\text{Long-term}) = \frac{15 + 10 + 5}{100} = \frac{30}{100} = 0.30

c) To find the probability that the same client does not own shares in a stock fund:
First, find the probability of owning shares in a stock fund (both moderate and high-risk):

P(\text{Stock fund}) = P(\text{Moderate-risk stocks}) + P(\text{High-risk stocks}) = \frac{25 + 18}{100} = \frac{43}{100} = 0.43

Then, find the complement:

P(\text{Not stock}) = 1 - P(\text{Stock fund}) = 1 - 0.43 = 0.57

The answers are:
a)

0.07

0.30

0.57

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