31. A group of 25 commuters regularly use the PARK AND RIDE transport for going to work. The facility consists of three parking lots, A, B and C. Suppose that the probability that lot A is chosen is .5, the prob- ability that B is chosen is 4 and the probability that C is chosen is .1. (a) What is the probability that 17 cars will be parked in lot A and 6 will be parked in lot B? What is the expected number of cars that will be parked in lot A? in lot B? in lot C? (b)
a)
This means we get 17 in A, 6 in B, and 2 in C.
Hence, by multinomial probability,
P(17,6,2) = [25!/(17!6!2!)](0.5)^17 (0.4)^6 (0.1)^2
= 0.009463781 [ANSWER]
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b)
E(xA) = n p(A) = 25*0.5 = 12.5 [ANSWER]
E(xB) = n p(B) = 25*0.4 = 10 [ANSWER]
E(xC) = n p(C) = 25*0.1 = 2.5 [ANSWER]
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