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A draws a card from a pack of `n` cards marked `1,2,ddot,ndot` The card is replaced in the pack and `B` draws a card. Then the probability that `A` dr

Monjur Alahi

A draws a card from a pack of `n` cards marked `1,2,ddot,ndot` The card is replaced in the pack and `B` draws a card. Then the probability that `A` draws a higher card than `B` is `(n+1)2n` b. `1//2` c. `(n-1)2n` d. none of these
A. `(n + 1)//2n`
B. `1//2`
C. `(n - 1)//2n`
D. none of these


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Salim Ahmed Kawsar

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Correct Answer - C
If A draws card higher than B, then the number of favorable cases is (n - 1) + (n + 2) + … + 3 + 2 + 1 (as when B draws card number 1, then A can draw any card from 2 to n and so on). Therefore, the required probability is
`(n((n-1))/(2))/(n^(2)) = (n-1)/(2n)`

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