Question
Class 12MathematicsProbability

Find the probability of drawing a diamond card in each of the two consecutive draws from a well shuffled pack of cards, if the card drawn is not replaced after the first drawn.

Verified Answer

Let A = event of drawing a diamond card in the first draw

Let B = event of drawing a diamond card in the second draw

P(A) = (¹³C₁) / (⁵²C₁) = 13/52 = 1/4

After drawing a diamond card in the first draw, 51 cards are left out of which 12 are diamond cards.

∴ P(B/A) = (¹²C₁) / (⁵¹C₁) = 12/51 = 4/17

Now, Required Probability = P(A ∩ B)

= P(A) × P(B/A)

= (1/4) × (4/17)

= 1/17