Exactly two heads out of six coins

Text

Six fair coins are tossed at the same time. What is the probability of getting exactly $2$ heads?

Solution

Each outcome is a string of $6$ symbols H/T, all equally likely: the possible cases are $2^{6}=64$. The favorable cases are the strings with exactly $2$ heads, i.e. the ways to choose which $2$ of the $6$ coins land heads: $\binom{6}{2} = 15.$ Hence $P = \frac{\binom{6}{2}}{2^{6}} = \frac{15}{64} \approx \boxed{0.234}.$