The formula for the expected value is:
[tex]E(X)=\sum x_iP(x_i),[/tex]where x_i are the possible values and P(x_i) the probabilities.
We are given that 3 envelops contain a $496 check, therefore, the probability of choosing a $496 check is:
[tex]\frac{3}{6}=\frac{1}{2}.[/tex]Analogously, we get that the probability of choosing a $1020 check is 1/2.
Therefore:
[tex]E(X)=496(\frac{1}{2})+1020(\frac{1}{2})=758.[/tex]