** 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)**