Answer to Question #301935 in Discrete Mathematics for Tege

Question

6. Team A has probability 2/3 of winning whenever it plays.suppose A plays four Games.find the probability p that A wins more than half of its gamed.

Answer 1

Let $X=$ the number of games won: $X\sim Bin (n, p).$

Given $p=2/3, n=4, q=1-p=1/3.$

$P(X\ge3)=P(X=3)+P(X=4)$

$=\dbinom{4}{3}(\dfrac{2}{3})^3(\dfrac{1}{3})+\dbinom{4}{4}(\dfrac{2}{3})^4=\dfrac{16}{27}$