A store sells two different brands of dishwasher soap, and each brand comes in t

Question

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 table. 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 B1S)? What are the probabilities of the other brand-size combinations? (Fill up the table.)

Size S M L Brand B1 0.80 B2 0.20 0.20 0.70 0.10

Explanation / Answer

Solution:

Size S M L Brand B1 0.8*0.2= 0.16 0.8*0.7= 0.56 0.8*0.1 =0.08 0.8 B2 0.2*0.2= 0.04 0.7*0.2 =0.14 0.1*0.2 = 0.02 0.20 0.20 0.70 0.10 1.00

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