What is the probability of getting the sum as 4 or 7 or 12 when two dice are thrown simultaneously?

Explanation

Two dice thrown simultaneously
`therefore` Total no. of elementary events = `6xx6=36`
Let A be the "getting the sum 4"
B be the event "getting the sum 7" and
C be the event "getting the sum 12", then
A{(1, 3), (3, 1), (2, 2)},
`implies " " P(A)=3/36`
B = {(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)}
`implies " " P(B)=6/36`
C={6, 6}
`implies " " P(C)=1/36`
Now, `(PcupBcupC)=P(A)+P(B)+P(C) " " [therefore` A, B and C are mutually exclusive events]
`=(3)/(36)+(6)/(36)+(1)/(36)`
`=(10)/(36)`
`=(5)/(18)`
Thus, the required probability, `P(AcupBcupC)=(5)/18)`