Question

Fifteen coupons are numbered $1, 2....... 15$, 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

• A. $\bigg(\frac{9}{16}\bigg)^6$
• B. $\bigg(\frac{8}{15}\bigg)^7$
• C. $\bigg(\frac{3}{5}\bigg)^7$
• D. None of these

Answer 1

Answer: (D)

Since, there are $15$ possible cases for selecting a coupon and seven coupons are selected, the total number of cases of selecting seven coupons $= 15^7$
It is given that the maximum number on the selected coupon is $9$, therefore the selection is to be made from the coupons numbered $1$ to $9$.
This can be made in $97$ ways. Out of these $9^7$ cases, $8^7$ does not contain the number $9$.
Thus, the favourable number of cases $= 9^7 - 8^7$.
$\therefore \, \, $ Required probability $=\frac{9^7 -8^7}{15^7}$