The probability of an outcome A is 1/6 . The probability of the B outcome is 1/4 . If the probability of A or B or both is 1/12 . What is the probability of both outcomes A and B?
A
1/2
B
1/3
C
2/5
D
3/4
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
Prob.(A outcome) = \(\frac{1}{6}\), Prob.(B outcome) = ¼
P(A ∪ B) = 1/12, Prob.(A ∩ B)
Prob.(A ∩ B) = Prob.(A) + Prob.(B) − Prob.(A ∪ B)
1/6 + 1/4 − 1/12
= (2 + 3 − 1) ÷ 12
= 4/12
= 1/3
Prob.(A ∩ B) = 1/3
Source: Myschool Past Questions Archive (Record #41288)