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

#### Solution

In a pack of 52 cards, there are 13 diamond cards.

Let event A: The first card drawn is a diamond card.

∴ P(A) = (""^13"C"_1)/(""^52"C"_1)

= 13/52

= 1/4

Let event B: The second card drawn is a diamond card.

Since the first diamond card is kept aside, we now have 51 cards, out of which 12 are diamond cards.

∴ Probability that the second card is a diamond card under the condition that the first diamond card is kept aside in the pack

= "P"("B"/"A")

= (""^12"C"_1)/(""^52"C"_1)

= 12/51

= 4/17

∴ Required probability = P(A ∩ B)

="P"("B"/"A")"P"("A")

= 1/4 xx 4/17

= 1/17

Concept: Conditional Probability
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