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Computing Probabilities

A retail grocer has decided to market organic "health foods" and will purchase a new line of products from each of two suppliers. Unknown to the grocer, the two suppliers are in financial distress. Past experience has shown that, for firms with similar credit histories, the probability that bankruptcy proceedings will be initiated within one year is .7. We are interested in observing the financial progress of the two suppliers over the next year. For this experiment, the simple events and their associated probabilities are as follows (B1: Supplier 1 declares bankruptcy; N1: Supplier 1 does not declare bankruptcy, etc.): Simple Events are (B1, B2), (B1, N2), (N1, B2), (N1, N2) with associated probabilities of .49, .21, .21, and .09 respectively.

Compute the probabilities of each of the following events:

D: {Neither supplier declares bankruptcy}
F: {At least one supplier declares bankruptcy during the next year}

I have not been able to figure this problem out. Can you show how do work this problem out? Thanks.

Solution Preview

Before we begin a problem such as this one, the first thing that we need to do is to check to see what information is relevant to the calculation and what is not. In this problem, note that there is information ...

Solution Summary

This solution provides a step-by-step answer to the probability problem.

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