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?
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To find the expected value of a roll, we need to multiply each outcome by its probability and then sum them up.
1. Calculate the probability of each outcome:
- Number 10 appears on four sides, so the probability of rolling a 10 is 4/10 = 0.4.
- Number 5 appears on three sides, so the probability of rolling a 5 is 3/10 = 0.3.
- Number 25 appears on two sides, so the probability of rolling a 25 is 2/10 = 0.2.
- Number 27 appears on one side, so the probability of rolling a 27 is 1/10 = 0.1.
2. Multiply each outcome by its probability:
Expected value = (10 x 0.4) + (5 x 0.3) + (25 x 0.2) + (27 x 0.1)
Expected value = 4 + 1.5 + 5 + 2.7
3. Sum up the results:
Expected value = 13.2
Therefore, the expected value of a roll in this game is 13.2.