Question

The probability of winning a game is 20% if you play 20 times how many times should you excpect to win?

Answer 1

You should win 40 times

Answer 2

Given that the probability of winning a game is 20%. The number of games won out of 20 follows binomial probability distribution.

The probability distribution/mass function is

$P(X=x)=C(n,x)p^x(1-p)^{n-x},x=0,1,2,3,...,n$. Here $n=20,p=0.2$

The expected value of X is

$E(X)=np=20*0.2=4$