Ex 13.2, 2 - Class 12

Transcript

Ex 13.2, 2 Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the Probability that both the cards are black. Two cards are drawn at random without replacement from a pack of 52 cards, we need to find the Probability that both the cards are black Let the events be E : first card drawn is black F : second card drawn is black Probability both the cards drawn are black = Probability first card drawn is black × Probability second card drawn is black, given first card drawn is black So, P(E ∩ F) = P(E) × P(F|E) Now, P(E) = Probability first card drawn is black There are 26 black cards in a pack of 52 cards ∴ P(E) = 26﷮52﷯ = 1﷮2﷯ P(F|E) = Probability second card drawn is black, given first is black If first card drawn is black, 51 cards are left in the pack and out of them, 25 black cards are left ∴ P(F|E) = 25﷮51﷯ Now, P(E ∩ F) = P(F|E) × P(E) = 25﷮51﷯ × 1﷮2﷯ = 𝟐𝟓﷮𝟏𝟎𝟐﷯ ∴ Probability that both cards drawn are black is 25﷮102﷯