Customers at a gas station pay with a credit card A debit ca

Customers at a gas station pay with a credit card (A), debit card (B), or cash (C). Assume that successive customers make independent choices with

P(A) = 0.6, P(B) = 0.2, and P(C) = 0.2.(a) Among the next 100 customers, what are the mean and variance of the number who pay with a debit card? (b) Answer part (a) for the number among the 100 who don\'t pay with cash.

Solution

a)

Note that

variance = n p (1 - p)

here,

p = probability of debit card = 0.6. Thus,

variance = 100(0.6)(1-0.6) = 24 [answer]

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b)

Note that

variance = n p (1 - p)

here,

p = probability of not cash = 1 - p(cash) = 1 - 0.2 = 0.8.

Thus,

variance = 100(0.2)(1-0.2) = 16 [answer]