Explanation

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