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

Options

A. `(n + 1)//2n`
B. `1//2`
C. `(n - 1)//2n`
D. none of these

Answer

C

Explanation

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)`