Question

If P(high) = 0.3, P(low) = 0.7, P(favorable | high) = 0.9, and P(unfavorable | low) = 0.6, then P(favorable) =

a. 0.10
b. 0.27
c. 0.30
d. 0.55

Answer 1

After calculating the conditional probability for a favorable outcome given a low state and applying the total probability theorem, the correct answer for the probability of a favorable outcome is 0.55. Option d

Step-by-step explanation:

The question provided involves calculating the probability of a favorable outcome given different probabilities for high and low states and the respective conditional probabilities for those states. The formula for total probability is needed here, which states that:

P(favorable) = P(favorable | high)P(high) + P(favorable | low)P(low)

To find P(favorable | low), we need to use P(unfavorable | low) since only favorable and unfavorable outcomes are possible, and their probabilities sum up to 1. So, we have:

P(favorable | low) = 1 - P(unfavorable | low) = 1 - 0.6 = 0.4

Then:

P(favorable) = (0.9)(0.3) + (0.4)(0.7) = 0.27 + 0.28 = 0.55

Therefore, the correct answer is d. 0.55.