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Fifteen coupons are numbered 1, 2, ........ 15 respectively seven coupons are selected at random one at time with eplacement. The probability that the largest number appearing on a selected coupons is 9 is

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${(\frac{3}{5})}^{7}$

${(\frac{8}{15})}^{7}$

${(\frac{9}{16})}^{6}$

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

answer is D.

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Detailed Solution

Seven coupons are selected from 15 coupons with replacement $n (S) = 15^{7}$

E= Largest no. appearing is 9

$n (E) =$ (each time coupons 1-9)-(each time

selected coupons (1-8))

$\begin{array}{rcl} = & 9^{7} - 8^{7} \\ P (E) & = & \frac{9^{7} - 8^{7}}{15^{7}} \end{array}$

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