0 votes
in Probability by (17.9k points)
closed by

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) \(\frac{4}{13}\) 


(d) \(\frac{7}{13}\) 

1 Answer

+1 vote
by (17.1k points)
selected by
Best 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)

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.