We know that the expected value of win is given by
[tex]E\left [ x \right ]=\sum_{i=1}^{n}x_if(x_i)[/tex]
Now, from the given directions, we have
[tex]x_1= 40, f(x_1)=50, x_2=60, f(x_2)=100[/tex]
On substituting these, values we get
[tex]E(x)=50\times 0.40 + 100\times 0.60\\ E(x)=\$ 80[/tex]
Therefore, the expected value of the prize is $80
