Question

15 coupons are numbered 1,2,3,.........,15 respectively. 7 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. ${\left(\frac{9}{16}\right)}^6$
• B. ${\left(\frac{8}{15}\right)}^7$
• C. ${\left(\frac{3}{5}\right)}^7$
• D. $\frac{9^7-8^7}{{15}^7}$

Answer 1

The correct option is D $\frac{9^7-8^7}{{15}^7}$

Given , 7 coupons are selected from 15 coupons one at a time with Replacement.
Total no.of all cases$={15}^7$
For the maximum of number to be 9, the coupons to be selected from the set {1,2,3,4,5,6,7,8,9}.
No.of selections can be done for 7coupons among these set$=9^7$
But for maximum of number to be 9 among these case, we have to subtract all the cases which 9 is involved.
For 9 to be not involved,then selecting 7 coupons among the set excluding $9=8^7$
$\therefore$ Total no.of required selection in which 9 is the maximum$=(9^7-8^7)$
Probability of selecting 7 coupons from the set with replacement of which 9 is maximum$=\frac{(9^7-8^7)}{{15}^7}$