Suppose that the chance of having both a favorable survey and an unsuccessful product launch is 0.2.In addition,the frequency of favorable market surveys for all new product launches is 0.5.Then the chance of a successful product launch given a favorable survey is:
A)0.8
B)0.5
C)0.4
D)0.6
E)0.3

Question

Quizplus · Accepted Answer

We can use Bayes' Theorem to solve the problem. Let S denote a favorable survey and P denote a successful product launch. Then we want to find P(P|S), the probability of a successful product launch given a favorable survey. Bayes' Theorem states that:

P(P|S) = P(S|P) * P(P) / P(S)

where P(S|P) is the probability of a favorable survey given a successful product launch, which we don't know. But we can use the fact that P(S) = P(S|P) * P(P) + P(S|not P) * P(not P), where not P denotes an unsuccessful product launch. We know that P(S|not P) = 0.5 - 0.2 = 0.3, since the frequency of favorable market surveys is 0.5 and the chance of having both a favorable survey and an unsuccessful product launch is 0.2. We also know that P(not P) = 1 - P(P), since the two outcomes are mutually exclusive and exhaustive. Putting everything together, we get:

P(S) = P(S|P) * P(P) + 0.3 * (1 - P(P))
0.5 = P(S|P) * P(P) + 0.3 - 0.3 * P(P)
0.2 * P(P) = 0.2
P(P) = 1

So we have P(S) = P(S|P) * 1 + 0.3 * 0 = P(S|P), which means that P(S|P) = 0.5. Therefore, using Bayes' Theorem, we get:

P(P|S) = 0.5 * 1 / 0.5 = 1

So the chance of a successful product launch given a favorable survey is 1 or 100%, which corresponds to choice D.

Suppose That the Chance of Having Both a Favorable Survey