Question

Fifteen coupons are numbered $1,2,3,...,15.$ Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on the selected coupon is $9,$ is

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

Answer 1

Answer: (B), (D)

The correct options are
B ${\left(\frac{3}{5}\right)}^7$
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.

Thus total number of favorable ways are $9^7-8^7$

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