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Two cards are drawn at random without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.

1 Answer

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Best answer

Describe the events as follows

B1: ‘getting a black card in the first draw.’

B2: ‘getting a black card in the second draw.’

P(B1) = \(\frac{26}{52} = \frac{1}{2}\)

When the first event is executed and since no replacement is allowed, the remaining total number of cards become 51 and black cards become 25.

P(B2/B1) = \(\frac{25}{51}\)

Therefore the required probability

P(B1 ∩ B2) = P(Bl) × P(B2/B1) =

\(\frac{1}{2} \times \frac{25}{51} = \frac{25}{102}.\)

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