Question 1:

(a) 75 percent of all people in a population are vaccinated against a par-ticular disease. During an epidemic, the probability that a vaccinated person is infected is 0.12, whereas the probability that a non-vaccinated person is infected is 0.35. Use a tree diagram to show this information.

(i) Evaluate the probability that a random chosen person will be infected during the epidemic.

(ii) During the epidemic, a person chosen at random was found to be not infected. Determine the probability that he was not vaccinated.

Question 2:

In the mass production of bolts, it is found that 5% are defective. Bolts are selected at random and put into packets of ten.

A packet is selected at random. Find the probability that it contains

(i) three defective bolts.
(ii) at most three defective bolts.
Two packets are selected at random.
(iii) Evaluate the probability that there are no defective bolts in eitherpacket.

Question 3:

A book containing 500 pages has 750 misprints.

(i) What is the average number of misprints per page?
(ii) Find the probability that page 427 contains more than the average number of misprints.
(iii) Find the probability that pages 427 and 428 will contain no mis-prints.