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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