Probability of getting either a sum of 8 or at least one 4 in the roll of a pair dice

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Sum of 8 equal to 5/36 shown here.

At least one 4 means one of three scenarios:

1. (4, not 4) = 1/6 * 5/6 = 5/36
2. (not 4, 4) = 5/6 * 1/6 = 5/36
3. (4, 4) = 1/6 * 1/6 = 1/36

The phrase "or", means we add both probabilities (sum of 8) and (at least one 4):
5/36 + (5/36 + 5/36 + 1/36)
16/36

Simplify by dividing each part of the fraction by 4
4/9