Find the indicated probablities, using the geometric distribution, the Poisson d

Question

Find the indicated probablities, using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual. If convenient, use the appropriate probability table or technology to find the probabilities.Assume the probability that you will make a sale on any given telephone call is 0.12. Find the probability that you (a) make your first sale on the fifth call, (b) make your sale on the first, second, or third call, and (c) do not make a sale on the first three calls.

Explanation / Answer

answer

Let the xth call be the call that the first sale is made. The support is then x = 1,2,3,4,5,.... .
===> Use the geometric distribution with pmf

P(x)=(1-p)x-1 *p

=(0.88)x-1 *0.12

a) P(5)=(0.88)4 *0.12

=0.07196

b) P(1)+P(2)+P(3)

=0.12+0.88*0.12+0.88^2*0.12

=0.12+0.1056+0.09292

=0.31852

C) 1-P(1)-P(2)-P(3)

=1-0.31852

=0.68148

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