Q. 45.0( 2 Votes )

# Two cards are drawn successively without replacement from a well-shuffled deck of 52 cards. Find the probability of exactly one ace.

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(A1) = P(Drawing ace from 52 cards deck)

P(O1) = P(Drawing cards other than ace from 52 cards deck)

P(A2) = P(Drawing ace from remaining 51 cards deck)

P(O2) = P(Drawing a card other than ace from remaining 51 cards deck)

We need to find the probability of drawing exactly one ace

P(DA) = P(Drawing exactly 1 ace in the drawn two cards)

P(DA) = 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(DA) = (P(A1)P(O2)) + (P(O1)P(A2))

The required probability is .

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