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

⇒ P(D_RB) = 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(D_RB) = (P(R₁)P(B₂)) + (P(B₁)P(R₂))

⇒

⇒

⇒

∴ The required probability is .