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#