Given:
A standard 6-sided dice is rolled.
If you roll an even number you get two points.
If you roll an odd number you lose one point.
To find:
The expected number of points per roll?
Solution:
If a dice is rolled, then the possible outcomes are 1, 2, 3, 4, 5, 6.
Odd values are 1, 3, 5 and the even values are 2, 4, 6.
The probability of getting an odd number is:
[tex]P(odd)=\dfrac{3}{6}[/tex]
[tex]P(odd)=\dfrac{1}{6}[/tex]
The probability of getting an even number is:
[tex]P(even)=\dfrac{3}{6}[/tex]
[tex]P(even)=\dfrac{1}{6}[/tex]
The expected number of points per roll is:
[tex]E(x)=2\times P(even)-1\times P(odd)[/tex]
[tex]E(x)=2\times \dfrac{1}{2}-1\times \dfrac{1}{2}[/tex]
[tex]E(x)=1-0.5[/tex]
[tex]E(x)=0.5[/tex]
Therefore, the expected number of points per roll is 0.5.
