Question

Suppose that 54% of the people who inquire about investments at a certain brokerage firm end up investing in stocks, 33% end up investing in bonds, and 68% end up investing in stocks or bonds (or both). What is the probability that a person who inquires about investments at this firm will invest in both stocks and bonds?

Answer 1

The probability that a person who inquires about investments at this firm will invest in both stocks and bonds is 19 %

Explanation:

The union probability of events is equal to the sum of the individual probabilities, minus the probability of the intersection event.

In our case we want the probability intersection (the probability of investments in both stocks and bonds)

• Probability of investments in stocks (PS) = 54 % or
  `(54)/(100)`

• Probability of investments in bonds (PB) = 33 % or
  `(33)/(100)`

• Probability of investments in stocks or bonds (union probability) (PSoB) = 68 % or
  `(68)/(100)`

• Probability of investments in stocks and bonds (PSaB)

PSoB = PS + PB - PSaB

PSaB = PS + PB - PSoB

PSaB =
`(54)/(100) +(33)/(100)-(68)/(100)`

PSaB =
`(19)/(100)`

PSaB = 19 %

The probability that a person who inquires about investments at this firm will invest in both stocks and bonds is 19 %