What is the expected mover per spin

[Guest]

James has designed a board game that uses a spinner with ten equal sectors numbered 1 - 10. If the spinner stops at an odd number, a player moves forward double that number of squares. However, if the spinner stops on an even number, the player must move back half that number of squares.

a) what is the expected mover per spin?

What I did was make a chart first.

# landed on spaces moved prob
1 2 1/10 for all (2)1/10
2 1 (1) 1/10
3 6
4 2 etc
5 10
6 3
7 14
8 4
9 18
10 5


I then added them together, 0.2+ 0.1+0.6+0.2+1+0.3+1.4+0.4+1.8+0.5= 6.5*1/10=0.65

Isnt that how you find the answer for this type of question? The answer is "forward 3.5 squares."

 

[Guest]

oh no, you cant do big spaces on this? now my chart is probably hard to understand? If so, tell me, and ill re do it on a program and copy it onto here then.

 

[soroban]

Hello, Anna!

James has designed a board game that uses a spinner with ten equal sectors numbered 1 - 10.
If the spinner stops at an odd number, a player moves forward double that number of squares.
If the spinner stops on an even number, the player must move back half that number of squares.

a) What is the expected moves per spin?

You forgot that some moves are backwards.


\(\displaystyle \begin{array}{ccccc}\text{# landed on} &\;\;\; & \text{spaces moved} & \;\;\; & \text{prob} \\ \\ \\
\hline \\
1 & & 2 & & 1/10 \\ \\
2 & & -1 & & " & \\ \\ \\
3 & & 6 & & " & \\ \\ \\
4 & & -2 & & " & \\ \\ \\
5 & & 10 & & " & \\ \\ \\
6 & & -3 & & " & \\ \\ \\
7 & & 14 & & " & \\ \\ \\
8 & & -4 & & " & \\ \\ \\
9 & & 18 & & " & \\ \\ \\
10 & & -5 & & " &
\end{array}\)

\(\displaystyle E \:=\:2(\frac{1}{10})\,-\,1(\frac{1}{10})\,+\,6(\frac{1}{10}) - 2(\frac{1}{10})\.+\.10(\frac{1}{10})\,-\,3(\frac{1}{10}\,+\,14(\frac{1}{10})\,-\,4(\frac{1}{10})\,+\,18(\frac{1}{10})\,-\,5(\frac{1}{10})\)

. . \(\displaystyle = \:0.2 \,-\,0.1\,+\,0.6\,-\,0.2\,+\,0.8\,-\,0.3\,-\,1.4\,-\,0.4\,+\,1.8\,-\,0.5 \;=\;\fbox{+\,3.5}\)


A player can expect to move forward an average of 3.5 squares per turn.