# 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?

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 .

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