Question

9 out of 10 people at a game are rooting for the home team. What is the probability that exactly 6 of 8 people sitting together are rooting for the home team?

Answer 1

A random supporter roots the home team with probability 0.9, and the away team with probability 0.1.

Choosing 6 out of 8 supporters who root for the home team has probability

$\displaystyle\binom{8}{6}\cdot 0.9^6\cdot 0.1^2 = 28\cdot0.531441\cdot 0.01=0.14$