## Question

The minimum number of times a fair coin must be tossed so that the probability of getting at least one head is at least 0.8 is

### Solution

3

Suppose the coin is tossed *n* times. Let *X* be the number of heads obtained. Then *X* follows a binomial distribution with parameters *n* and *p *= 1/2. We have *P*(*X* ≥ 1) ≥ 0.8

⇒ 1 – *P*(*X* = 0) ≥ 0.8

This show that the least value of *n* is 3.

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