Question

Suppose that 65% of the people who inquire about investments at a certain brokerage firm end up investing in stocks, 38% end up investing in bonds, and 36% end up investing in both stocks and bonds. What is the probability that a person who inquires about investments at this firm will invest in stocks or bonds (or both)?

Answer 1

0.67 = 67% probability that a person who inquires about investments at this firm will invest in stocks or bonds (or both).

Explanation:

This question is solved treating these probabilities as Venn events.

I am going to say that:

Event A: Person invests in stocks.

Event B: Person invests in bonds.

65% of the people who inquire about investments at a certain brokerage firm end up investing in stocks

This means that
`P(A) = 0.65`

38% end up investing in bonds

This means that
`P(B) = 0.38`

36% end up investing in both stocks and bonds.

This means that
`P(A \cap B) = 0.36`

What is the probability that a person who inquires about investments at this firm will invest in stocks or bonds (or both)?

This is
`P(A \cup B)`, given by the following equation:

`P(A \cup B) = P(A) + P(B) - P(A \cap B)`

Considering the values we have for this problem:

`P(A \cup B) = 0.65 + 0.38 - 0.36 = 0.67`

0.67 = 67% probability that a person who inquires about investments at this firm will invest in stocks or bonds (or both).