A pair of dice is thrown. Find the probability of obtaining a sum of 8...
Let the events be defined as:
A: Obtaining a sum of 8
B: Getting an even number on both dice
P(A U B) = P(A) + P(B) – P (A ∩ B)
Now cases favourable to A are (3, 5) (5, 3) (2, 6) (6, 2) (4, 4)
So, P(A) = 5/36
Cases favourable to B: (2, 2), (2, 4), (2, 6), (4, 2), (4, 4), (4, 6), (6, 2), (6, 2), (6, 4), (6, 6).
P(B) = 9/36
Now, (2, 6) (6, 2) and (4, 4) are common to both events A and B
So, P (A ∩ B) = 3/36
⇒ P (A ∪ B) = (5/36) + (9/36) – (3/36) = 11/36