If black hair, brown hair, and blond hair are equally likely (and no other hair colors can occur), what is the probability that a family of 3 children has at least two blondes?

There are a total of \(3^3 = 27\) outcomes (by the multiplication rule: there are 3 colors for 3 children). There are \(\binom{3}{2} \cdot 2 = 6\) ways to have exactly 2 blondes and we need to add one more way (all blondes) to the final result to get \(\frac{\binom{3}{2} \cdot 2 + 1}{3^3} = \frac{7}{27}\)