stat question in description!

Question

A basketball team has won 70% of its games so far this season. What is the probability that it will win 8 of its next 10 games?

Answer 1

We assume that the probability of winning a game is 70% and that the games are independent.  Then the probability of winning 8 games is 0.7⁸, and the probability of losing two games is 0.3², so the probability of winning 8 games and losing two games is their product, 0.7⁸0.3².  But there are C(10,8) = 10!/(8!2!) ways for the basketball gods to choose 8 of the 10 games to be wins, and each way has probability 0.7⁸0.3², so the total probability is C(10,8)0.7⁸0.3² .

 

Or, if you prefer the fancy notation and terminology, this is the probability P(X = 8) where X ~ Bin(10,0.7), or X is binomially distributed with 10 trials and 0.7 probability of success.