Consider a group of 10 life insurance policies, seven of which are on male lives and

three of which are on female lives. Three of the 10 policies are chosen at random

(one after the other, without replacement).

Find the probability that the three selected policies are all on male lives.

(b) A survey showed that 40% of investors invest in at least two companies in order to

diversify their risk. Find an approximate probability that more than 100 investors

have invested in at least two companies in a random sample of 300 investors.

(c) The human resources department of a large company currently estimates that 82%

of new employees recruited by their call centres will still be employed by the com-

pany after one year. A recent extension to the call centre business led to 280 new

employees being recruited.

Calculate an approximate value for the probability that at least 240 of these new

employees will still be employed by the company after one year.