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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

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 \[\leq 9\] .

\[p = \frac{9}{15} = \frac{3}{5}\]
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 =
\[\left( \frac{3}{7} \right)^7 - \left( \frac{8}{15} \right)^7\]
  Is there an error in this question or solution?
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APPEARS IN

 RD Sharma Solution for Mathematics for Class 12 (Set of 2 Volume) (2018 (Latest))
Chapter 33: Binomial Distribution
MCQ | Q: 17 | Page no. 29
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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 Concept: Bernoulli Trials and Binomial Distribution.
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