\(W\) be the amount of money (in dollars) won by an entry. Then
\begin{equation*}
\begin{aligned}
E[W] = \amp 10000000\cdot P(W = 10000000) + 350000 \cdot P(W = 350000) + 50000 \cdot P(W = 50000)\\
\amp + \, 20000 \cdot P(W = 20000) +500 \cdot P( W = 500) + 60 \cdot P( W = 60)\\
\amp = \frac{10000000}{300000000} + \frac{350000}{150000000} + \frac{50000}{80000000} + \frac{20000}{5000000} + \frac{500}{800000} + \frac{60}{7000} \\
\amp = 0.0494880952380952
\end{aligned}
\end{equation*}
So the expected value of the amount won by one entry in the sweepstakes is about 5 cents. (b) Let
\(X\) be the net earnings from one entry into the sweepstakes. Then
\(X = W - 0.34\text{,}\) so
\begin{equation*}
E[X] = E[W- 0.34] = E[W] - 0.34 = -0.290511904761905.
\end{equation*}
Hence, taking into account the cost of postage, there is an expected loss of about 29 cents from one entry into the sweepstakes.