How many times must a man toss a fair coin so that the probability of having at least one head is more than 90%?

Question

Philoid · Accepted Answer

Let us assume that, man tosses the coin n times. Thus, n tosses are the Bernoulli trials

∴ Probability of getting head at the toss of the coin

Let us assume,

∴

It is given in the question that,

Probability of getting at least one head >

∴

1 – P (x = 0) > 0.9

(i)

Hence, the minimum value of n satisfying the given inequality = 4

∴ The man have to toss the coin 4 or more times