Question

Fifteen coupons are numbered 1 to 15. Seven coupons are selected at random, one at a time with replacement. The probability that the largest number appearing on selected coupon be 9 is

• A. ${\left(\frac{1}{15}\right)}^7$
• B. ${\left(\frac{8}{15}\right)}^7$
• C. ${\left(\frac{3}{5}\right)}^7$
• D. None of these

Answer 1

The correct option is D None of these

Total ways$={\left(15\right)}^7$
For favorable ways, we must select $7$ coupons
numbered from $1$ to $9$ so that $9$ is selected atleast once.
The total number of favorable ways are $9^7-8^7$
$\Rightarrow$ Required probability $=\frac{9^7-8^7}{{15}^7}$