Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
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The Least Number of Times a Fair Coin Must Be Tossed So that the Probability of Getting at Least One Head is at Least 0.8, is (A) 7 (B) 6 (C) 5 (D) 3 - Mathematics

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MCQ

The least number of times a fair coin must be tossed so that the probability of getting at least one head is at least 0.8, is

Options

  • 7

  • 6

  • 5

  • 3

     
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Solution

3

Let X denote the number of coins. 
Then, X follows a binomial distribution with

\[p = \frac{1}{2} , q = \frac{1}{2}\]
\[\text{ It is given that } P(X \geq 1) \geq 0 . 8\]
\[ \Rightarrow 1 - P(X = 0) \geq 0 . 8\]
\[ \Rightarrow P(X = 0) \leq 1 - 0 . 8 \]
\[ \Rightarrow P(X = 0) = 0 . 2\]
\[ \Rightarrow \frac{1}{2^n} \leq 0 . 2 \]
\[ \Rightarrow 2^n \geq \frac{1}{0 . 2}\]
\[ \Rightarrow 2^n \geq 5\]
\[\text{ This is possible when n } \geq 3\]
\[\text{ So, the least value of n is }  3 .\]

Concept: Bernoulli Trials and Binomial Distribution
  Is there an error in this question or solution?

APPEARS IN

RD Sharma Class 12 Maths
Chapter 33 Binomial Distribution
MCQ | Q 11 | Page 28

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