Question

A coin is tossed n times. The probability of getting head at least once is greater than 0.8, then the least value of n is

• A. 2
• B. 3
• C. 5
• D. 4

Answer 1

Answer: (B)

3

Answer 2

Let X be the number of heads getting in n tossed. Therefore X follows binomial distribution with parameters
$n , p = \frac{1}{2} , q = \frac{1}{2}$.
Given that $P(X \geq 1) \geq 0.8$
$\therefore \, \, 1 - P(X = 0) \geq 0.8$
$\Rightarrow \, \, P(X = 0) \leq 0.2$
$\Rightarrow ^{n}c_{0} \frac{1}{2} ^{n} \frac{1}{2} ^{0} \le 0.2$
$\Rightarrow \frac{1}{2^{n}} \le \frac{1}{5}$
$\Rightarrow 2^{n} \ge 5$
$\therefore \, \,$ The least value of n is 3.