In reviewing retirement portfolios, Kim determined the probability of a client owning stock is 0.50 and the probability of owning a bond is 0.20. The probability of a customer who owns bonds already owning stock is 0.55. What is the probability a client owns both securities in their retirement portfolio?
A) 0.30
B) 0.40
C) 0.39
D) 0.28

Question

Quizplus · Accepted Answer

The probability of owning both securities is found by multiplying the probability of owning a bond by the conditional probability of owning stock given that the client owns a bond: 0.20 * 0.55 = 0.11. However, none of the options match this calculation, suggesting a mistake in my initial explanation. Correctly, the probability a client owns both securities is found by using the given probabilities correctly. The correct calculation should involve understanding the relationship between the probabilities given, but without the exact calculation provided in the options, there's an error in my explanation. Re-evaluating with the correct approach: The probability of a client owning both a stock and a bond is indeed found by multiplying the probability of owning a bond (0.20) by the probability of a bond owner also owning stock (0.55), which correctly calculates to 0.11, not directly matching any of the provided choices due to a mistake in my initial response. The correct approach involves applying the formula for conditional probability correctly, but it seems there was a misunderstanding in the application of the probabilities provided in the question.

In Reviewing Retirement Portfolios, Kim Determined the Probability of a Client