Question

A card is drawn from a well shuffled deck of cards. What is the probability of getting a king, given that the card drawn is black. (a) \(\frac{1}{13}\) (b) \(\frac{4}{13}\) (c)\(\frac{6}{13}\) (d) \(\frac{7}{13}\) Select the correct answer from above options

Answer 1

Answer: (a) \(\frac{1}{13}\) Let S be the sample space of drawing a card out of 52 cards. Then, n(S) = 52 Let A: Event of drawing a king ⇒ n(A) = 4 (A pack has 4 kings) B: Event of drawing a black card ⇒ n(B) = 26 (A pack has 26 black cards) A ∩ B: Event of drawing a king of a black card ⇒ n(A ∩ B) = 2 (A pack has 2 black kings) \(\therefore P(A) =\frac{4}{52}= \frac{1}{13}\) ,\( P(B) =\frac{26}{52}= \frac{1}{2}\) , \(P(A\,\cap\,B) = \frac{2}{52} = \frac{1}{26}\) P(Getting a king, given card is drawn is black \(P(A/B) =\frac{P(A\,\cap\,B)}{P(A)} =\frac{1/26}{1/2} =\frac{2}{26}\) \(\frac{1}{13}\) (∵ Event A depends on B)