Peter is playing a game where a ten-sided die is rolled. Four sides of the die have the number 10, three sides of the die have the number 5, two sides of the die have the number 25, and one side of the die has the number 27.
What is the expected value of a roll?
4/10 chance of rolling 10
3/10 chance of rolling 5
2/10 chance of rolling 25
1/10 chance of rolling 27
Expected value is the sum of the outcomes multiplied by probabilities
= (4/10)(10) + (3/10)(5) + (2/10)(25) + (1/10)(27)
To find the expected value of a roll, we need to multiply each outcome by its probability and sum them all up.
Let's calculate the probability of each outcome first:
- The probability of rolling a 10 is 4/10 = 2/5.
- The probability of rolling a 5 is 3/10.
- The probability of rolling a 25 is 2/10 = 1/5.
- The probability of rolling a 27 is 1/10.
Now, let's calculate the expected value.
E(X) = (10 * (2/5)) + (5 * (3/10)) + (25 * (1/5)) + (27 * (1/10))
= (20/5) + (15/10) + (25/5) + (27/10)
= 4 + 1.5 + 5 + 2.7
= 13.2
Therefore, the expected value of a roll in this game is 13.2.