Question:

Two cards are drawn from a deck of cards in which one card is missing. It is known that the drawn cards are both club cards. Find the probability that the missing card is a club card.

Updated On: Aug 21, 2024
  • 14\frac{1}4
  • 34\frac{3}{4}
  • 1150\frac{11}{50}
  • 1350\frac{13}{50}
  • 950\frac{9}{50}
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The Correct Option is C

Solution and Explanation

There are two possibilities, the missing card is a club card or the missing card is not a club card. The probability that the missing card is a club card is ¼, and the probability that it is not a club card is ¾.

Case I: When the missing card is a club card:
The probability that the two cards drawn are club cards = 12C251C2=12×1151×50\frac{12C_2}{51C_2} = \frac{12\times11}{51\times50}

Case II: When the missing card is not a club card:
The probability that the two cards drawn are club cards = 13C251C2=13×1251×50\frac{13C_2}{51C_2} = \frac{13\times12}{51\times50}
By Baye’s Rule,
The required probability = 14×12×1151×5014×12×1151×50+34×13×1251×50=1150\frac{\frac{1}{4}\times\frac{12\times11}{51\times50} }{ \frac{1}{4}\times\frac{12\times11}{51\times50}+\frac{3}{4}\times\frac{13\times12}{51\times50 }}= \frac{11}{50}

Hence, option C is the correct option.

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