Question

Michael is playing a game in which he spins a spinner with 6equal-sized slices number1 through6. The spinner stops on a numbered slice at random

Answer 1

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;

`\begin{gathered} (1)/(6)+(1)/(2)+(5)/(6)+(7)/(6)-(5)/(24)-(5)/(24) \\ =(13)/(6)+(1)/(2)-(5)/(24)-(5)/(24) \\ =(13)/(6)+(1)/(2)+(-10)/(24) \\ =(13)/(6)+(1)/(2)-(5)/(12) \\ =(13)/(6)+(1)/(2)-(5)/(12) \\ =(26+6-5)/(12) \\ =(27)/(12) \\ =(9)/(4)=\text{ \$}2.25 \end{gathered}`

Answers;

`\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}`