Step 1
Given;
The spinner has 6 equal-sized slices, so each slice has a 1/6 probability of showing up.
The table below will be used to calculate the expected value.
The expected value will be;
[tex]\begin{gathered} \frac{1}{6}+\frac{1}{2}+\frac{5}{6}+\frac{7}{6}-\frac{5}{24}-\frac{5}{24} \\ =\frac{13}{6}+\frac{1}{2}-\frac{5}{24}-\frac{5}{24} \\ =\frac{13}{6}+\frac{1}{2}+\frac{-10}{24} \\ =\frac{13}{6}+\frac{1}{2}-\frac{5}{12} \\ =\frac{13}{6}+\frac{1}{2}-\frac{5}{12} \\ =\frac{26+6-5}{12} \\ =\frac{27}{12} \\ =\frac{9}{4}=\text{ \$}2.25 \end{gathered}[/tex]
Answers;
[tex]\begin{gathered} A)Expected\text{ value of playing the game = \$2.25} \\ B)\text{ Michael can expected to gain Money} \\ He\text{ can expect to win 2.25 per spin} \end{gathered}[/tex]
