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  • A draws two cards at random from a pack of 52 cards. After returning them to the pack and shuffling it, B draws two cards at random. The probability that their draws contain exactly one common card

A draws two cards at random from a pack of 52 cards. After returning them to the pack and shuffling it, B draws two cards at random. The probability that their draws contain exactly one common card is

Option: 1

\frac{25}{546}


Option: 2

\frac{50}{663}


Option: 3

\frac{25}{663}


Option: 4

None of these


Answers (1)

best_answer

The probability of both drawing the common card x

\mathrm{=P(x)=}(probability of A drawing the card x and any other card y) X
(probability of B drawing the card x and a card other than y )

\mathrm{\therefore \quad P(x)=\frac{{ }^{51} C_1}{{ }^{52} C_2} \times \frac{{ }^{50} C_1}{{ }^{52} C_2}} for all x, where x has 52 values.

\therefore the required probability\mathrm{=\Sigma P(x)=52 \times \frac{51 \times 50 \times 4}{52 \times 51 \times 52 \times 51}=\frac{50}{663}}

Posted by

avinash.dongre

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