# 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 - Mathematics

MCQ

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

Let p= probability that a selected coupon bears number $\leq 9$ .

$p = \frac{9}{15} = \frac{3}{5}$
n = number of coupons drawn with replacement
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) = $^ {7}{}{C}_7 p^7 q^0 = \left( \frac{3}{7} \right)^7$
Similarly, probability that largest number on the selected coupon bears the number $\leq 8$ will be

P(X=7) = $^{7}{}{C}_7 p^7 q^0 = \left( \frac{8}{15} \right)^7$
(since, p will become $\frac{8}{15}$)
Hence required probability will be =
$\left( \frac{3}{7} \right)^7 - \left( \frac{8}{15} \right)^7$
Concept: Bernoulli Trials and Binomial Distribution
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#### APPEARS IN

RD Sharma Class 12 Maths
Chapter 33 Binomial Distribution
MCQ | Q 17 | Page 29