6.56 A store sells two different brands of dishwasher soap, and each brand comes in three different sizes: small

(S), medium (M), and large (L). The proportions of the two brands and of the three sizes purchased are displayed as marginal totals in the following table.

Size S M L B1 .40 Brand B2 .60

.30 .50 .20 Suppose that any event involving brand is independent of any event involving size. What is the probability of the event that a randomly selected purchaser buys the small size of Brand B1 (the event B1 > S)?

What are the probabilities of the other brand–size combinations?