Question

Fifteen coupons are numbered $1,\mathrm{2.......15}$, 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. $(\frac{9}{16}{)}^6$
• B. $(\frac{8}{15}{)}^7$
• C. $(\frac{3}{5}{)}^7$
• 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 $=\frac{9^7-8^7}{15^7}$