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

$(\frac{3}{5})^7$

As the largest number can be atmost 9, for each section there are 9 favourable coupons i.e. 1, 2, 3, 4, 5………………

⇒ Number of favourable ways = 9⁷ (7 coupons are to be selected)

Total ways =15⁷ because for each selection these are 15 possible coupons.

Probability = $(\frac{9}{15})^7=(\frac{3}{5})^7$