Q. 114.3( 3 Votes )

Two cards are drawn from a well shuffled pack of 52 cards, one after another without replacement. Find the probability that one of these is red card and the other a black card?

Answer :

Given that two cards are drawn from a well-shuffled deck of 52 cards.


We know that there will 26 Red and 26 Black cards present in a deck.


It is told that two cards successively without replacement.


Let us find the probability of drawing the cards.


P(R1) = P(Drawing Red card from 52 cards deck)




P(B1) = P(Drawing Black card from 52 cards deck)




P(R2) = P(Drawing Red card from remaining 51 cards deck)




P(B2) = P(Drawing Black card from remaining 51 cards deck)




We need to find the probability of drawing exactly one Red and one black card


P(DRB) = P(Drawing exactly one red and one black card)


P(DRB) = P(Drawing Red first and Black next) + (P(Drawing Black first and red next)


Since drawing cards are independent their probabilities multiply each other,


P(DRB) = (P(R1)P(B2)) + (P(B1)P(R2))





The required probability is .


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :