Answer to Question #101356 in Statistics and Probability for ray

Question

1) Life insurance salesman meets his prospective customers separately. At each meeting, he makes the same effort to persuade the prospective client to be insured. The vendor's understanding after a long term in the insurance business is that the probability of persuading the customer to be insured (probability of success) is 0,1. What is the probability in 4 trials to insure one of them?

Answer 1

As probability of success p = 0.1,

Probability of failure q = 1 - p

= 1 - 0.1 = 0.9

Number of trials = 4

Number of success = 1

Now formula for binomial distribution with x success out of n trials.

P(x) = ⁿC_x * p^x * q^n-x

P(x = 1) = ⁴C₁ * 0.1¹ * 0.9³ = 0.2916