Question 1

(a) Suppose E is a sample and P and Q are events, when are P and Q

(i) Independent

(ii) Mutaully exclusive

(iii) Exhaustive.

(b) A company has two machines A and B for making computers. It has been observed

that machine A produces 20% of the total production of computers while machine

B produces 80% of the total production of computers. Suppose that 5% of all the

computers produced by A are defective while 10% of all the computers produced

B are defective. What is the probability that a computers taken at random from a

day's production was made by the machine A given that it is defective?

(c) Financial Planning Consultants Inc. keeps track of 500 stocks. Table below classifies

the stocks according to two criteria. Three hundred are from the New York exchange

and 200 are from the American exchange. Two hundred are up, 100 are unchanged,

and 200 are down,

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