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tutorial2

# tutorial2 - randomly and the colours are recorded(a Find...

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THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTURIAL SCIENCE STAT 1301 PROBABILITY AND STATISTICS I EXAMPLE CLASS 2 1. A and B are two events. Suppose that 6 . 0 ) | ( = B A P , 3 . 0 ) | ( = A B P and 72 . 0 ) ( = B A P . Let a A P = ) ( . (a) Express ) ( B A P and ) ( B P in terms of a . (b) Using the results of (a), or otherwise, find the value of a . (c) Are A and B independent events? Explain your answer briefly. 2. A and B are two events. Suppose that 4 3 ) | ( P = A B , 5 3 ) | ( P = B A and 5 2 ) ( P = A , where A and B are complementary events of A and B respectively. Let p B = ) ( P , where 1 0 < < p . (a) Find ) ( P B A . (b) Express ) ( P B A in terms of p . (c) Using the fact that B A is the complementary event of B A , or otherwise, find the value of p . (d) Are A and B mutually exclusive? Explain your answer.

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