The expected value is calculated by:
[tex]E(x)=x_1p_1+x_2p_2+x_3p_{3\ldots}[/tex]x represents the value and p the probability.
For this problem we need to know how many possibilities for you to roll 2 odd numbers, 2 even numbers and to get nothing.
As can be seen in the diagram above, the probability of obtaining two even numbers is:
[tex]P(even)=\frac{9}{36}=0.25[/tex]And for two odd numbers:
[tex]P(odd)=\frac{9}{36}=0.25[/tex]And to get nothing:
[tex]P(nothing)=\frac{18}{36}=0.5[/tex]Then the expected value must be:
[tex]E(x)=2\cdot0.25+2\cdot0.25-1\cdot0.5[/tex][tex]E(x)=0.5[/tex]At this booth the school makes money because the expected value for the player is less than what is worth to play.
