#### 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

7

6

5

3

#### Solution

3

Let *X* denote the number of coins.

Then, *X* follows a binomial distribution with

\[p = \frac{1}{2} , q = \frac{1}{2}\]

\[\text{ It is given that } P(X \geq 1) \geq 0 . 8\]

\[ \Rightarrow 1 - P(X = 0) \geq 0 . 8\]

\[ \Rightarrow P(X = 0) \leq 1 - 0 . 8 \]

\[ \Rightarrow P(X = 0) = 0 . 2\]

\[ \Rightarrow \frac{1}{2^n} \leq 0 . 2 \]

\[ \Rightarrow 2^n \geq \frac{1}{0 . 2}\]

\[ \Rightarrow 2^n \geq 5\]

\[\text{ This is possible when n } \geq 3\]

\[\text{ So, the least value of n is } 3 .\]

Is there an error in this question or solution?

Solution 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 Concept: Bernoulli Trials and Binomial Distribution.