A financial analyst chooses two investment assets at random, one after another without replacement, from a portfolio consisting of technology stocks and utility stocks. The probability of achieving a target return depends on the composition of the selected assets:
- If both selected assets are technology stocks, the probability of achieving the target return is .
- If exactly one selected asset is a technology stock, the probability of achieving the target return is .
- If neither selected asset is a technology stock, the probability of achieving the target return is .
What is the probability, expressed as a decimal, that the analyst achieves the target return?
Answer: 0.55
Answer
The probability that the analyst achieves the target return is 0.55.
To find the overall probability of achieving the target return, calculate the probability of each mutually exclusive composition of assets selected without replacement, and weight each by its conditional probability of success. The probability of selecting two technology stocks is (3/5) * (2/4) = 0.30. The probability of selecting one technology stock and one utility stock in either order is (3/5)*(2/4) + (2/5)*(3/4) = 0.60. The probability of selecting two utility stocks is (2/5) * (1/4) = 0.10. Multiplying each by its respective success rate (0.80, 0.50, and 0.10) yields 0.24 + 0.30 + 0.01 = 0.55.
Step-by-Step Solution
Key Concept
Probability of Dependent Events and Law of Total Probability
Estimated Time:2m 0s