The Town-Pump service station has performed an analysis of its customers and fou

Question

The Town-Pump service station has performed an analysis of its customers and found that 85% pay on credit and the rest pay cash. We are interested in finding the probability distribution of the random variable, X, when X is defined as the number of cash paying customers when four customers are selected at random. That is, find each of the probability of X=0, X=1, X=2, and X=3 under the conditions given by constructing a trials table similar to those constructed in class. Note: There are two outcomes (cash or credit) on each trial (each customer sampled), there are four trials (four customers sampled), so there will be 2x2x2x2=24 = 16 outcomes (rows on the table).

Explanation / Answer

I wont draw the table as they are very difficult to draw here,but i can give you steps. a) X=0 (no cash paying customer ) = 1/16 (only one favorable condition) b) X=1 (1 cash paying customer ) = 4/16 =1/4 (4 favorable condition,one at each position) c) X=2 (2 cash paying customer ) = 6/16 =3/8 (6 favorable condition) d) X=3 (3 cash paying customer ) = 4/16 =1/4 (4 favorable condition, one credit card customer at 4 different position)

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