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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 a selected coupon is 9 is
Options
\[\left( \frac{3}{5} \right)^7 \]
\[\left( \frac{1}{15} \right)^7\]
\[\left( \frac{8}{15} \right)^7\]
None of these
Solution
Answer: None Of these
Let p= probability that a selected coupon bears number \[\leq 9\] .
X = number of coupons bearing number \[\leq 9\]\ Probability that the largest number on the selected coupons does not exceed 9
= probability that all the coupons bear number \[\leq 9\]
P(X=7) = \[^{7}{}{C}_7 p^7 q^0 = \left( \frac{8}{15} \right)^7\]
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