At least one head out of five coins

Text

Five fair coins are tossed at the same time. What is the probability of getting at least one head?

Solution

It is convenient to use the complementary event: “at least one head” is the opposite of “no heads” (all tails). The possible outcomes are $2^{5}=32$, and only one is “all tails”, so $P(\text{no heads}) = \frac{1}{32}.$ Therefore $P(\text{at least one head}) = 1 - \frac{1}{32} = \frac{31}{32} \approx \boxed{0.969}.$