A card is drawn from a well shuffled deck of cards. What is the probab

1.	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) \(\frac{7}{13}\)
Answer» 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)

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) \(\frac{7}{13}\)

Answer»

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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