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Questions  

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

a
(n+1)/2n
b
1/2
c
(n-1)/2n
d
none of these

detailed solution

Correct option is 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 isn(n−1)2n2=n−12n

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A bag contains 10 different balls. Five balls are drawn simultaneously and then replaced and then seven balls are drawn. If the probability that exactly three balls are common to the two draws is p, then the value of 8p is ________.


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