sports team named Philadelphia Streets has a probability of (2/3) for winning each game against their division rivals Hockeytown. They play 12 games against each other during the season. Assume that the outcome of any particular game is independent from an outcome of any other game. Let X be the random variable that stands for the number of wins that Philadelphia Streets will have in those 12 games. What is the expected value of X?

For each game, the Philadelphia Streets team can only have two outcomes. Either they win, or they do not win. The outcome of any particular game is independent from an outcome of any other game. This means that we can solve this problem using concepts of the binomial probability distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes, with probability p, on n repeated trials, and X can only have two outcomes.

The expected value of X is given by the multiplication of p and n.

In this problem, we have that:

They play 12 games, so [tex]n = 12[/tex].

Philadelphia Streets has a probability of (2/3) for winning each game against their division rivals Hockeytown, so [tex]p = \frac{2}{3}[/tex].

What is the expected value of X?

[tex]E(X) = 12*\frac{2}{3} = 8[/tex]