A4. Two events A and B have probabilities P(A) 0.3 and P(B) 0.5. For each of the

Question

A4. Two events A and B have probabilities P(A) 0.3 and P(B) 0.5. For each of the following statements state whether they could be true or not, justify your answers and in each case give P(AnB): (a) A and B are mutually exclusive; (b) B is a subevent of A (i.e. B C A); (c) A and B are independent. A5. Suppose that a mortgage company classifies borrowers into two classes_high risk and low risk. Records indicate that high risk clients have a 20% chance of defaulting in any year, while for low risk clients the chance is only 10%. If 20% of the company's business is with high risk clients, what proportion of clients default in any given year? If Mr Kenny did not default in 2016, what is the probability that he is a low risk client? A6. The random variable X has probability density function otherwise (a) Find the value of k such that this is a proper probability density function. (b) Calculate P(X 1

Explanation / Answer

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A5) High risk default = 0.2

Low risk default = 0.1

Proportion of client default = 0.2 * 0.2 + 0.1 * 0.8

P = 0.12

12% of the clients default.

This means P(no default) = 0.88

So, P(Kenny is low risk|Did not default) = (0.8 * 0.9)/0.88

P = 0.82

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