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

Answer: (D)

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

Given: 15 coupons from 1 to 15. 7 coupons are selected with replacement

To find: the probability that the largest number appearing on a selected coupon is 9

Sol: According to the question,

Favourable numbers possible is {1, 2, 3, 4, 5, 6, 7, 8, 9}

Hence total possible ways of drawing 7 numbers with largest number being 9 = $9^7-8^7$

Hence the probability that the largest number appearing on a selected coupon is 9 = $\frac{9^7-8^7}{{15}^7}$