Question

Find the indicated probabilities 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 0.15. 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.

Answer 1

(a)

Geometric Distribution

p = probability of sale = 0.15

q = 1 - p = 0.85

P(first sale on 5th call) = q⁴ p

                               = 0.85⁴ X 0.15

                                 = 0.0783

So,

Answer is:

0.0783

(b)

P(First OR Second OR Third) = P(First) + P(Second) + P(Third)

                                          = p + qp + q² p

                                       = 0.15 + (0.85 X 0.15) + (0.85² X 0.15)

                                         = 0.15 + 0.1275 + 0.1084

                                         = 0.3859

So,

Answer is:

0.3859

(c)
P(Failure in First three calls) = q³

                                         = 0.85³

                                          = 0.6141

So,

Answer is:

0.6141