A survey found that 65 of callers complain about the service

A survey found that 65% of callers complain about the service they receive from a call center. State the assumptions and determine the probability of each event described below.

1) The next three consecutive callers complain about the service.
2) The next two callers complain but not the third.
3) Two out of the next three calls produce a complaint.
4) None of the next 10 calls produces a complaint.

Solution

# Assumption: B. The events of different calls resulting in a complaint are independent.

# The Probability that a caller complain about the sevice is 0.61 =p,say .

(a) Probability of the next three calls being with complaint is -

P(1st call will lodge a complaint AND 2nd call AND 3rd call will also lodge a complaint) = p*p*p = p³ =0.226981 = 0.227 (approx.)

(b) Probability that the next two caller will complain and not the third one

=p*p*(1-p) = 0.61²*0.39 =0.14511 = 0.145 (approx.)

(c) Probability that Two of the next three calls will show up with complaint,

₃C₂ * p²*(1-p) = 3*0.61²*0.39 = 3*0.14511 = 0.43533 = 0.435 (approx.)

(d) None of the next 10 callers willnot complain ,

(1-p)¹⁰ = 0.39¹⁰=0.0000814 = 0.0001 (approx.)