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Make-up Class Test (with solution)

Make-up Class Test (with solution) - 10/11 THE UNIVERSITY...

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10/11 p. 1 THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1301 Probability and Statistics I Class Test (Makeup) Answer all questions. Time allowed: 1 hour Name ______________________ Student ID _________________ Class ___________ 1. [10 marks] Suppose that a box contains one blue card without any label, and four red cards labeled A , B , C and D . Two of these five cards are selected at random, without replacement. (a) If it is known that card A has been selected, what is the probability that both cards are red? (b) If it is known that at least one red card has been selected, what is the probability that both cards are red? Ans: (a) Total number of possible outcomes of the two selected cards is . 10 2 5 = If card A is drawn, the combination of the two cards must be one of (A,Blue), (A,B), (A,C), (A,D). Therefore ( ) 4 . 0 10 4 drawn is A card = = P Similarly, if card A and another red card are drawn, the combination must be one out of (A,B), (A,C), (A,D) and hence ( ) 3 . 0 10 3 drawn is A card red cards both = = P Thus ( ) ( ) ( ) drawn is A card drawn is A card red cards both drawn is A card | red cards both P P
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