Fifteen coupens are numbered `1,2,3,...15` respectively. Seven coupons are selected at random one at a time with replacement The Probability that the largest number appearing on a selected coupon is 9 is :

Explanation

No. of Coupons `=15`

`7` Coupons are selected with replacement. So, total ways `= 15^7`

Now, for `9` to be the largest in selected coupons, so coupons should be selected from `1, 2, ldots 9`

Out of these `9` Coupons, in `7` chances, we can select in `9^7` ways.

But this will also include cases when `9` is not selected at all, and thus, the highest number that is selected in `8`.

This can be done in `8^7` ways (i.e `8` coupons in `7` chances)

Thus, favourable cases for 9 to be largest in the selected coupon, number of cases `= 9^7 – 8^7`

Required Probability` = (9^7 – 8^7)/15^7`