A select two cards at random from a pack of 52 cards. After returning them to the pack and shuffling it, B selects two cards at random. The probability that their draws contain exactly one common card is:a)b)c)d)e)Correct answer is option 'B'. Can you explain this answer?

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

Correct answer is option 'B'. Can you explain this answer?

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A select two cards at random from a pack of 52 cards. After returning...

Given that, A select two cards at random from a pack of 52 cards. After returning them to the pack and shuffling it, B selects two cards at random.

Now, according to the question, A can select 2 cards in ⁵²C₂ ways. B can select one of these in ²C₁ ways and 1 of the remaining 50 in ⁵⁰C₁ ways.

Therefore, required probability =

Hence, the correct option is (B).

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