InterviewSolution
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InterviewSolution
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A card is drawn at random from a well shuffled pack of 52 cardsX : The card drawn is black or a king Y : The card drawn is a club or heart or a jack Z : The card drawn is an ace or a diamond or a queen Then, which of the following is correct. (a) P(X) > P(Y) > P(Z) (b) P(X) ≥ P(Y) = P(Z) (c) P(X) = P(Y) > P(Z) (d) P(X) = P(Y) = P(Z) |
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Answer» (c) P(X) = P(Y) > P(Z) P(X) = \(\frac{26}{52}\) + \(\frac{4}{52}\) - \(\frac{2}{52}\) = \(\frac{28}{52}\) (∵ There are 26 black cards, 4 kings and 2 black kings) P(Y) = \(\frac{13}{52}\) + \(\frac{13}{52}\) + \(\frac{4}{52}\) - \(\frac{1}{52}\) - \(\frac{1}{52}\) = \(\frac{28}{52}\) (∵ There are 13 clubs, 13 hearts and 4 jacks, 1 jack of clubs and 1 jack of hearts) P(Z) = \(\frac{4}{52}\) + \(\frac{13}{52}\) + \(\frac{4}{52}\) - \(\frac{1}{52}\) - \(\frac{1}{52}\) = \(\frac{19}{52}\) (∵ There are 4 aces, 13 diamonds, 4 queens, 1 ace of diamond, 1 queen of diamond) ∴ P(X) = P(Y) > P(Z). |
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