Question

A card from a pack of 52 card is lost From remaining cards of the pack, two cards are drawn found to be both diamonds. Find probability of the lost card being a diamond.

Answer 1

Let Events E₁ = Lost card is diamond 

E₂ = Lost card is not diamond 

The number of diamond card = 13 out of 52 cards.

∴ P(E₁) = ¹³C₁/⁵²C₁ = 13/52 = 1/4

and 39 cards are not diamonds

∴ Probability P(E₂) = 39/52 = 3/4

(i) When a card of diamond lost there remaining cards of diamond are 12 out of 52

∴ P(A/E₁) = ¹²C₂/⁵¹C₂ = (12 x 11)/(51 x 50)

Here A represents the cards lost. 

(ii) When diamond card is not 

Lost then probability of drawing 2 cards of diamond

P = ¹³C₂/⁵¹C₂ = (13 x 12)/(51 x 50)

∴ Probability that lost card is a diamond

Hence, required probability = 11/50