Question

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

   

Answer 1

3

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

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