Question

If P(high) = .3, P(low) = .7, P(favorable | high) = .9, and P(unfavorable | low) = .6, then P(favorable) =

a. .10
b. .27
c. .30
d. .55

Answer 1

The probability of a favorable outcome is calculated using the law of total probability, which takes into account all possible scenarios that lead to a favorable outcome. After computing, we determine that P(favorable) is 0.55.

Step-by-step explanation:

To find P(favorable), we can use the law of total probability, which in this case states that:

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

We know that P(favorable|high) = 0.9, P(high) = 0.3, and P(low) = 0.7. To find P(favorable|low), we use the fact that P(favorable|low) = 1 - P(unfavorable|low), since an outcome can only be either favorable or unfavorable. Given P(unfavorable|low) = 0.6, we calculate P(favorable|low) = 1 - 0.6 = 0.4.

Now, substituting the known values we get:

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

So the correct answer is d. 0.55.