Statistics and Probability

A retail grocer has decided to market organic "health food" 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 will be initiated one year is .7.  We are interested in observing the financial progress of the two supplies over the next year.

For this experiement, the simple events and their associated probabilites are as follows (B1: Supplier 1 declares bankruptcy; N1: Supplier 1 does not declare bankruprcy, etc.):

The Simple Events (B1, B2),(B1, N2),
(N1, B2) and (N1, N2) have probabilities equal to .49,.21,.21, and .09 respectively.

Compute the probabilities of each of the following events:

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