A fair coin is tossed n - times such that the probability of...

When a coin is tossed, then probability of head, $P\left(\text{Head}\right) = P\left(\text{Tail}\right) = \dfrac{1}{2}$

Therefore, $1 - P$ (All tail)$\ge 0 . 9$

$⇒ 1 - {\left(\dfrac{1}{2}\right)}^{n} \ge 0 . 9$

$⇒ {\left(\dfrac{1}{2}\right)}^{n} \le \dfrac{1}{10}$

⇒ {n}_\min = 4 .