How many times must a man toss a fair coin, so that the probability of having at least one head is more than 80%?

Given; Tossing of a fair coin;

Let p be the probability of getting a head and q be the probability of getting a tail.

Let X be the random variable denoting the number of tosses.

According to the given condition:

P(X≥1) = 1 − P(X<1) >80%

⇒ P(X<1) < 1 − 0.8

⇒ P(X = 0) < 0.2

∴ 2ⁿ > 5

⇒ n ≥ 3

∴ The man should toss a fair coin minimum 3 times so that the probability of having at least one head is more than 80%