1. An engineering company advertises a job in three newspapers, A, B and C. It is known that these papers attract undergraduate engineering readerships in the proportions 2:3:1. The probabilities that an engineering undergraduate sees and replies to the job advertisement in these papers are 0.002, 0.001 and 0.005 respectively. Assume that the undergraduate sees only one job advertisement. If the engineering company receives only one reply to it advertisements, calculate the probability that the applicant has seen the job advertised in place A.

2. Obtain the sample space of an experiment that consists of a fair coin being tossed four times. Consider the following events: A is the event all four results are the same. B is the event exactly one Head occurs. C is the event at least two Heads occur. Show that P(A) + P(B) + P(C) = 17/16 and explain why P(A) + P(B) + P(C) > 1.

3. It is a fact that if A and B are independent events then it is also true that A' and B' are independent events. If A and B are independent events such that the probability that they both occur simultaneously is 1/8 and the probability that neither of them will occur is 3/8, find: a. the probability that event A will occur. b. the probability that event B will occur.

4. If A and B are two events associated with an experiment and P(A) = 0.4, P(A B) = 0.7 and P(B) = p, find: a. the choice of p for which A and B are mutually exclusive. b. the choice of p for which A and B are independent.