Question

At 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. None of these

Answer 1

Answer: (D)

None of these

Answer 2

Suppose the coin tossed $n$ times. Let $X$ be the number of heads obtained. Then $X$ follows a binomial distribution with parameters $n$ and $p = \frac { 1 } { 2 }$

We have, $P ( X \geq 1 ) \geq 0.8 \Rightarrow 1 - P ( X = 0 ) \geq 0.8$

⇒ $1 - { } ^ { n } C _ { 0 } P ^ { 0 } ( 1 - P ) ^ { n } \geq 0.8$

$\Rightarrow \left( \frac { 1 } { 2 } \right) ^ { n } \leq 0.2 \Rightarrow \left( \frac { 1 } { 2 } \right) ^ { n } = \frac { 1 } { 5 } \Rightarrow 2 ^ { n } \geq 5$

This shows that the least value of n is 3.