Maharashtra State BoardHSC Science (General) 11th
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From a pack of well-shuffled cards, two cards are drawn at random. Find the probability that both the cards are diamonds when the first card drawn is replaced in the pack - Mathematics and Statistics

Sum

From a pack of well-shuffled cards, two cards are drawn at random. Find the probability that both the cards are diamonds when the first card drawn is replaced in the pack

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Solution

Let A ≡ the event that first card is diamond

B ≡ the event that second card is also a diamond

Since the first card is replaced in the pack, the two events A and B are independent.

∴ P(A ∩ B) = P(A)·P(B)

The probability of drawing one diamond card out of 52 cards is  `13/52`.

∴ P(A) = P(B) = `13/52`

∴ P (both diamond cards) = P(A ∩ B)

= `13/52 xx 13/52`

= `1/16`.

Concept: Conditional Probability
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