# 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.

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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)