In testing a certain kind of truck tyre over rugged terrain, it is found that 75% of the trucks

complete test run without a blowout. Of the next 15 trucks tested, find the probability that

(i) exactly nine trucks complete the test run without blowout.

(ii) fewer than 11 trucks complete the test run without blowout.

(iii) more than 11 trucks complete the test run without blowout.

(b) On average, three traffic accidents per month occur at an intersection. What is the

probability that in any given month at least two accidents will occur at this intersection?

13.

(a) A computer network consists of 20 computers was attacked by a virus. Given that the

probability of the virus attacked a computer independently is 0.4. Find the probability that

(i) exactly seven computers will be attacked by the computer virus.

(ii) at least nine computers will be attacked by the computer virus.

(iii) between 11 and 14 (inclusive) computers will be attacked by the computer virus.

(b) The mean rate of new account initiated by customers using an internet service provider is

ten accounts per day. Find the probability that

(i) more than eight new accounts will be initiated today.

(ii) less than 16 accounts will be intitiated within two days.