1. The probability that a couple will have a child with black hair is 0.6.

If this couple has 7 children what is

(a) the probability that exactly 3 of these children have black hair ?

(b) the probability that no more than 2 of their children have black hair ?

(c) the probability that none of the children have black hair

(d) what is the mean number of their children that have black hair and what is the variance ?

2. The service life of an incandescent light bulbs used domestically was investigated.

It was found that a light bulb can last up to 3 years, and the probability distribution of the number of years a light bulb was used before failure is given below:

 (i) What is the mean service life of a light bulb?

(ii) What is the variance and standard deviation of a service life of a light bulb?