A financial analyst finds that 60% and 25% of his clients invest in the stock ma
ID: 3067298 • Letter: A
Question
A financial analyst finds that 60% and 25% of his clients invest in the stock market and the bond market respectively. It is also found that 15% of his clients invest in both markets. (a) Suppose that one of his clients is randomly selected, (i) what is the probability that the client has invested either in the stock market or in the bond market? (4 marks) (ii) what is the probability that the client has invested in the bond market but not in the stock market? (3 marks) (iii) what is the probability that the client has neither invested in the bond market nor in the stock market? (3 marks) (iv) if it is known that the client has not invested in the stock market, what is the probability that the client has neither invested in the bond market? (3 marks) With regard to the above situation, are the event of having invested in the stock market and the event of having invested in the bond market statistically independent? Explain briefly (b) (5 marks)Explanation / Answer
(a) (i) P(client has invested in either stock market or bond market) = P(stock market0 + P(bond market) - P(both)
= 0.6 + 0.25 - 0.15
= 0.7
(ii) P(bond market but not stock market) = P(bond market) - P(both)
= 0.25 - 0.15
= 0.10
(iii) P(client has invested in neither stock market nor bond market) = 1 - P(client has invested in either stock market or bond market)
= 1 - 0.70
= 0.30
(iv) P(not invested in bond market | not invested in stock market) = P(not invested in both)/ P(not invested in stock market)
= 0.30/(1 - 0.60)
= 0.75
(b) If A and B are independent, P(A) x P(B) = P(A & B)
Here, P(stock market) x P(bond market) = 0.6x0.25 = 0.15 = P(stock market and bond market)
So, the events are statistically independent.
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