Question

How many tosses of a fair coin are needed so that the probability of getting atleast one head is 0.875?

Answer 1

Solution.

Let $p = 0.875$ be the probability of getting at least one head. Let $q$ be the probability of getting all tails. It is logical that $p + q = 1.$ The coin is fair, so after tossing $n$ times the probability of of getting all tails is $q = 0.5^n$. So we get the equation:

$0.875+0.5^n = 1 \quad \Longrightarrow \quad n = \log_{0.5}(1-0.875) = 3$

Answer: 3