Answer:
The expected value of X is $0.2222.
Explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
For each dice, there are 6 possible outcomes(values from 1 to 6). So for 2 dices, there are
possible outcomes.
Desired outcomes:
Sum 5: (1,4), (2,3), (3,2), (4,1).
Sum 6: (1,5),(2,4),(3,3),(4,2),(5,1)
Sum 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1)
Sum of 9: (3,6), (4,5), (5,4), (6,3);
Sum of 12: (6,6)
Probabilities:
4 + 4 = 8 outcomes with a sum of 5 or 9.
8/36 = 2/9 probability of a sum of 5 or 9.
12 outcomes with a sum of 6, 7 or 12.
12/36 = 1/3 probability of the sum being 6, 7 or 12.
36 - 20 = 16 outcomes in which the sum is any other value. So
16/36 = 4/9 probability of a sum of any other value.
What is the expected value of X?
2/9 probability of earning $6.
1/3 = 3/9 probability of earning $2.
4/9 probability of losing $4.
Multiplying each outcome by its probability, we find the expected value. So
The expected value of X is $0.2222.