10 people enter an elevator with 40 floors above Assume that

10 people enter an elevator with 40 floors above. Assume that each person selects a floor to exit with equal probability and the selection of each person does not influence that of the others.

(a) What is the probability that either exactly 4 ppl get out on floor 35 or exactly 4 ppl get out on floor 36 (inclusive OR)?
(b) what is the probability that the elevator stops on floors 11, 15, and 39?

Solution

This is binomial probability distribution

n = 10 , p = 1/40

p(x) = nCx*(p)^x*(1-p)^(n-x)

a.) p(4) + p(4) = 2*10C4*(1/40)^4*(39/40)^6 = 0.00014094 = 1.4094 x 10^-4

b.) (1-(9/40)^10)^3 = 0.999999