Three Product Launches

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At a large company, the probabilities of success of three distinct new product launches are independently , , and , respectively. What is the probability that exactly two of the launches succeed?

Review: Three Product Launches


Explanation

In this question, if we call these launches A, B, and C, there are three possible ways that exactly two of the launches succeed. Case I: A fails, B and C succeed. Case II: B fails, A and C succeed. Case III: C fails, A and B succeed. We can compute the probability of each case, and then add them for the probability of the described result.

Case I:

Case II:

Case III:

The overall probability is thus .

The correct answer is (C).


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