Question

A random customer buys either brand A, brand B, or brand C with probabilities 0.25, 0.30, 0.35. There is a 0.10 probability that the customer will not buy anything. a) Of the next 4 customers, what is the probability that there will be at least one purchase each for brands A, B and C? b) What is the probability that the 3rd purchase of brand B is made before the 6th customer makes his purchase?

Answer 1

Explanation:

Given that a random customer buys as follows

A B C Nothing

Prob 0.25 0.30 0.35 0.10

a) Prob for atleast one customer out of 4 buying one = 1-Prob that all 4 do not buy =
`1- 0.1^4  =0.9999`

(since independent)

b) the probability that the 3rd purchase of brand B is made before the 6th customer makes his purchase

=prob that out of 6 customers atleast one purchase brand 3

= P(x>=1) where X = no of customers buying brand B and n = 6

Here X is binomial: p = 0.30 and q = 0.70

Hence P(X>=1) =
`1-q^6`

=
`1-0.7^6\\=0.8823`