The minimum number of times one has to toss a fair coin so that the probability of observing at least one head is at least 90 % is:

Step-by-step solution

Let a fair coin is tossed n times, then P ( at   least   one   head )   = 1 – P ( all   tails ) = 1 – 1 2 n > 90 100 (given) ⇒ 1 2 n < 1 - 90 100 = 1 10 ⇒ 2 n > 10 ⇒ n ≥ 4