Answer :

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

We know that there will 4 aces present in a deck.

It is told that two cards successively without replacement.

Let us find the probability of drawing the cards.

⇒ P(A_{1}) = P(Drawing ace from 52 cards deck)

⇒

⇒

⇒ P(O_{1}) = P(Drawing cards other than ace from 52 cards deck)

⇒

⇒

⇒ P(A_{2}) = P(Drawing ace from remaining 51 cards deck)

⇒

⇒

⇒ P(O_{2}) = P(Drawing a card other than ace from remaining 51 cards deck)

⇒

⇒

We need to find the probability of drawing exactly one ace

⇒ P(D_{A}) = P(Drawing exactly 1 ace in the drawn two cards)

⇒ P(D_{A}) = P(Drawing Ace first and others next) + (P(Drawing Other cards first and ace next)

Since drawing cards are independent their probabilities multiply each other,

⇒ P(D_{A}) = (P(A_{1})P(O_{2})) + (P(O_{1})P(A_{2}))

⇒

⇒

⇒

∴ The required probability is .

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