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A Coin is Tossed N Times. the Probability of Getting at Least Once is Greater than 0.8. Then, the Least Value of N, is (A) 2 (B) 3 (C) 4 (D) 5 - Mathematics

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MCQ

A coin is tossed n times. The probability of getting at least once is greater than 0.8. Then, the least value of n, is

Options

  • 2

  • 3

  • 4

  • 5

     
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Solution

3

Let X be the number of heads. Then X follows a binomial distribution with

\[p = \frac{1}{2}, q = \frac{1}{2}\]
\[\text{ Hence, the distribution is given by } \]
\[P(X = r) =^{n}{}{C}_r \left( \frac{1}{2} \right)^r \left( \frac{1}{2} \right)^{n - r} , r = 0, 1, 2, 3 . . . . . . n\]
\[ \therefore P(X \geq 1) = 1 - P(X = 0) \]
\[ = 1 - \left( \frac{1}{2} \right)^n \geq 0 . 8\]
\[\text{ Or } \  2^ n \geq \frac{1}{0 . 2}\]
\[ \Rightarrow 2^n \geq 5\]
\[\text{ This is possible only when n } \geq 3 . \]
\[\text{ So, the least value of n must be }  3 . \]

Concept: Bernoulli Trials and Binomial Distribution
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APPEARS IN

RD Sharma Class 12 Maths
Chapter 33 Binomial Distribution
MCQ | Q 24 | Page 29

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