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InterviewSolution
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All red face cards are removed from a pack of playing cards. The remaining cards are well, shuffled and then cards is drawn at random from them. Find the probability that the drawn cards is(i) a red card,(ii) A face card,(iii) a card of clubs. |
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Answer» Therefore are 6 red face cards. These are removed. Thus, remaining number of card = 52 - 6 = 46. (i) number of red cards now = 26 - 6 = 20. Therefore, P(getting a red card) = \(\frac{number\, of\,favorable\,outcomes}{number\,of \,all\,possible\,outcomes}\) = \(\frac{20}{46}\) = \(\frac{10}{23}\) Thus, the probability that the drawn card is a red card is \(\frac{10}{23}\). (ii) Number of face cards now = 12 - 6 = 6. Therefore, P(getting a face card) = \(\frac{number\, of\,favorable\,outcomes}{number\,of \,all\,possible\,outcomes}\) = \(\frac{6}{46}\) = \(\frac{3}{23}\). Thus, the probability that the drawn card is a face card is \(\frac{3}{23}\). (iii) The number of cards of clubs = 12. Therefore, P(getting a card of clubs) = \(\frac{number\, of\,favorable\,outcomes}{number\,of \,all\,possible\,outcomes}\) = \(\frac{12}{46}\) = \(\frac{6}{23}\) Thus, the probability that the drawn card is a card of clubs is \(\frac{6}{23}\). |
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