Question

36 Two cards are drawn at random from a pack of 52 cards. The probability that one of them is black and other is red is 26 13 13 1- 3) in 13 4) 204​

Answer 1

Answer:

We have three possible sequences of cards that satisfy your conditions (two black, one red): BBR, BRB and RBB. Let P(BBR),P(BRB),P(RBB) denote the probability that a randomly drawn sequence is of the form BBR, BRB and RBB respectively. The probability of three randomly drawn cards satisfying your condition is P(BBR)+P(BRB)+P(RBB). I will show you how to calculate P(BBR) and leave the rest to you.

When we draw the first card, there are 26 black cards and 52 cards total, so there is a 2652=12 chance that this card is black. If the first card is black, there are 25 black cards out of 51 total when we draw the second card, so there is a 2551 chance it is black. If the first two cards were both black, then there are 26 red cards out of 50 total when we draw the third card, so there is a 2650=1325 chance it is red. Thus P(BBR)=12⋅2551⋅1325=13102.