Question

A draws a card from a pack of n cards marked 1,2,3,....n. The card is replaced in the pack and B draws a card. Then find the probability that A draws a higher card than B.

Answer 1

Sample space { total number of cases } = n × n = n² [ because both A and B marked 1,2,3,4,...n}

A/C to question, A draws a higher card than B
Means if B draw card marked 1 then, possibilities of card A = (n - 1)
if B draws card marked 2 then, possibilities of card A = (n -2)
If B draw card marked 3 then, possibilities of card A = (n -3)
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If B draw card marked (n -1) , then possibility of card A = 1
So, number of favourable outcome /cases = (n -1) + (n -2) + (n -3) + ...... + 1
= (n - 1)(n -1+1)/2 = n(n -1)/2

Now, Probability = number of favourable outcomes/sample space
= n(n -1)/2n² = (n -1)/2n