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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3. A flower shop has 16 roses of which 3 are red, 6 are white and 7 are yellow. Mary selects 3 roses
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Unformatted text preview: randomly and the colours are recorded. (a) Find the probability that Mary selects exactly one red rose. (b) Given that Mary has selected exactly one red rose, find the probability that only one of the other two roses is yellow. 4. A teacher randomly selected 8 students from a class of 12 boys and 18 girls to form a group to take part in a flag-selling activity. (a) Find the probability that the group consists of at least 1 boy and 1 girl. (b) Given that the group consists of at least 1 boy and 1 girl, find the probability that there are more than 3 boys in the group....
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This note was uploaded on 01/16/2012 for the course STAT 1301 taught by Professor Smslee during the Fall '08 term at HKU.

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

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