Two card are drawn from a pack of playing cards, one after the other,

1.	Two card are drawn from a pack of playing cards, one after the other, find the probability of getting a queen in first and second draw .If the cards are drawn. (i) With replacement (ii) Without replacement
Answer» (i) with replace: there are 52 cards out of which 4 are queens ∴ Probability of getting a queen = \(\frac{4}{52}\) The card is replaced before the second draw. Again a card is drawn, getting a queen in the second draw = \(\frac{4}{52}\) ∴ Probability of getting two queens = \(\frac{4}{52}\)x \(\frac{4}{52}\)= \(\frac{1}{169}\) (ii) without replacement: when one card is not replaced there are 51 cards for the second draw with 3 queens. ∴ Probability of getting queen in second draw = \(\frac{3}{51}\) ∴ P(both queens) = Queen in 1st draw x queen in second draw \(=\frac{4}{52} \times \frac{3}{51} = \frac{12}{2625}\)

Two card are drawn from a pack of playing cards, one after the other, find the probability of getting a queen in first and second draw .If the cards are drawn. (i) With replacement (ii) Without replacement

Answer»

(i) with replace: there are 52 cards out of which 4 are queens

∴ Probability of getting a queen = \(\frac{4}{52}\)

The card is replaced before the second draw. Again a card is drawn, getting a queen in the second draw = \(\frac{4}{52}\)

∴ Probability of getting two queens = \(\frac{4}{52}\)x \(\frac{4}{52}\)= \(\frac{1}{169}\)

(ii) without replacement: when one card is not replaced there are 51 cards for the second draw with 3 queens.

∴ Probability of getting queen in second draw = \(\frac{3}{51}\)

∴ P(both queens) = Queen in 1st draw x queen in second draw

\(=\frac{4}{52} \times \frac{3}{51} = \frac{12}{2625}\)

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