What is the probability of getting either a sum of 8 or at least one 4 in the roll of a pair of dice?

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Answer 1 · 2016-10-27T14:55:01

The probability of either of the incidents happening is $5/12$ .

Here we consider two events: A - (finding a sum of $8$ ) & B (getting at least one $4$ )

A : Probability of A is $5/36$ because there are $7$ such events out of $6xx6=36$ events viz. $(2,6),(3,5),(4,4),(6,2),(5,3)$

B Probability of B is $11/36$ because there are $11$ such events out of $36$ events viz.

$(1,4),(2,4),(3,4),(4,4),(5,4),(6,4),(4,1),(4,2),(4,3),(4,5),(4,6)$ .

Now it is observed that the two incidents are not mutually exclusive as the incident resulting in $(4,4)$ is occurs in both.

Now, the probability of either of the incidents happening is

$P(AUB)=P(A)+P(B)-P(AnnB)$

i.e. $=5/36 +11/36 -1/36=15/36=5/12$