Question

A draws a card from a pack of cards numbered 1 to n. The card is replace in the pack and b draws a card. The probability that a draws a higher card than b is

Answer 1

Answer: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

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