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stat1301testsol

stat1301testsol - 11/12 THE UNIVERSITY OF HONG KONG...

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11/12 p. 1 THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1301 Probability and Statistics I Class Test October 28, 2011 1. [30 marks] Jim has a drawer containing four pairs of blue socks, three pairs of black socks, and two pairs of white socks. Suppose he pulls out two socks at random from the drawer. (a) What is the probability that Jim can draw a pair of socks with matched color? (b) If the first sock he drew is a white sock, what is the probability that the second sock he drew is also a white sock? (c) If one of the socks he drew is a white sock, what is the probability that the other sock he drew is also a white sock? Ans: (a) total number of possible pair of socks : 153 2 18 = C number of pair of socks with matched color : 49 2 4 2 6 2 8 = + + C C C ( ) 3203 . 0 153 49 color matched with socks of pair a draw randomly = = P (b) ( ) 1765 . 0 17 3 white is sock 1st | white is sock 2nd = = P (c) ( ) white is sock one least at | white are socks both P ( ) ( ) white is sock one least at white is sock one least at white are socks both P P = ( ) ( ) white is
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