Question

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

   

Answer 1

3

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

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