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)

None of these

Answer 2

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 $=\frac{9^7 -8^7}{15^7}$