Question

A mutual fund company offers its customers several different funds: a money market fund, three different bond funds, two stock funds, and a balanced fund. Among customers who own shares in just one fund, the percentages of customers in the different funds are as follows: $$ \begin{array}{lr} \text { Money market } & 20 \% \\ \text { Short-term bond } & 15 \% \\ \text { Intermediate-term bond } & 10 \% \\ \text { Long-term bond } & 5 \% \\ \text { High-risk stock } & 18 \% \\ \text { Moderate-risk stock } & 25 \% \\ \text { Balanced fund } & 7 \% \end{array} $$ A customer who owns shares in just one fund is to be selected at random. 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?

Short answer

a. The probability that the selected individual owns shares in the balanced fund is 7%. \ b. The probability that the selected individual owns shares in a bond fund is 30%. \ c. The probability that the selected individual does not own shares in a stock fund is 57%.

Step-by-step solution

Probability of owning shares in the balanced fund

The problem states that 7% of all customers own shares in the balanced fund. Therefore, if a customer is chosen at random, the probability of them owning shares in the balanced fund is also 7%. Since probability is the ratio of the number of favourable outcomes to the total number of possible outcomes, this simply translates the percentage into a probability.

Probability of owning shares in a bond fund

In order to find the probability that the selected individual owns shares in a bond fund, you need to add the probabilities of owning shares in each individual bond fund. From the data given, 15% own shares in the short-term bond, 10% own shares in the intermediate-term bond and 5% own shares in the long-term bond. The total probability here would be 15% + 10% + 5% = 30%, so the probability of owning shares in any bond fund is 30%.

Probability of not owning shares in a stock fund

In this case, we need to calculate the probability of the customer not owning shares in a stock fund. This is simply 1 (representing 100%) minus the total percentage of customers who own shares in a stock fund. From the data given, 18% own shares in high-risk stock and 25% own shares in moderate-risk stock. Thus, the probability of not owning shares in a stock fund = 100% - (18% + 25%) = 100% - 43% = 57%.