The expected value of the winnings is given by
[tex]E(x)=\sum x\cdot p(x)[/tex]Where x is the payout amount and p(x) is the corresponding probability.
[tex]\begin{gathered} E(x)=\sum x\cdot p(x) \\ E(x)=(1\cdot0.35)+(2\cdot0.2)+(5\cdot0.1)+(8\cdot0.2)+(10\cdot0.15)_{} \\ E(x)=0.35+0.4+0.5+1.6+1.5 \\ E(x)=4.35 \end{gathered}[/tex]This means that you are expected to get $4.35 in winnings.
Therefore, the expected value of the winnings is $4.35
