practice_problems/problems/unit-01/B-computing-probability-by-counting-outcomes/1

[giscus[bot]]

practice_problems/problems/unit-01/B-computing-probability-by-counting-outcomes/1

https://mids-w203.github.io/practice_problems/problems/unit-01/B-computing-probability-by-counting-outcomes/1.html

[dn7ucb]

(5+4+3+2+1+0) / (6 x 6) = 15/36 = 5/12

[Connor-Watson-Berkeley]

Let Gi = probability of rolling value i on the green die and R = probability that the value of the red die is larger than the value of the green die.

For any value i, P(Ri) = 1/6

Note the pattern. If the value of the red dice is 1 (i = 1), then the chance the green dice is larger is 5/6 (values 2-6 are larger). if i = 2, P(G) = 5/6, etc.

Therefore, P(G|Ri) = (6-i)/6

By the law of total probability + the multiplicative law:

P(G) = Sum(P(G|Ri)P(Ri) = 5/61/6+4/61/6+3/61/6+2/61/6+1/61/6+0/6*1/6 = 5/12