Dida bought a scratch ticket for $\$ 2.00$. The potential payoffs and probability of those payoffs are shown below. \begin{tabular}{|l|l|} \hline \multicolumn{1}{|c|}{ Value } & Probability \\ \hline$\$ 0.00$ & 0.15 \\ \hline$\$ 0.50$ & 0.50 \\ \hline$\$ 1.00$ & 0.20 \\ \hline$\$ 2.00$ & 0.10 \\ \hline$\$ 10.00$ & 0.05 \\ \hline \end{tabular} What is the expected value for the scratch ticket that Dida bought?

Step 1 ：Dida bought a scratch ticket for $2.00. The potential payoffs and probability of those payoffs are shown below.

Step 2 ：\begin{tabular}{|l|l|} \hline \multicolumn{1}{|c|}{ Value } & Probability \\ \hline $0.00 & 0.15 \\ \hline $0.50 & 0.50 \\ \hline $1.00 & 0.20 \\ \hline $2.00 & 0.10 \\ \hline $10.00 & 0.05 \\ \hline \end{tabular}

Step 3 ：The expected value of a random variable is the sum of the products of each outcome and its probability. In this case, the expected value of the scratch ticket is the sum of the products of each payoff and its probability.

Step 4 ：\[Expected Value = (0.00 \times 0.15) + (0.50 \times 0.50) + (1.00 \times 0.20) + (2.00 \times 0.10) + (10.00 \times 0.05)\]

Step 5 ：\[Expected Value = 1.15\]

Step 6 ：Final Answer: The expected value for the scratch ticket that Dida bought is \(\boxed{1.15}\)