Fewpal
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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) \(\frac{7}{13}\) 

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 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)

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