A sample space has two events A and B such that probabilities P(A ∩ B) = 1/2,…
2008
A sample space has two events A and B such that probabilities P(A ∩ B) = 1/2, P(A') = 1/3, P(B') = 1/3. What is P(A U B)?
- A.
11/12
- B.
10/12
- C.
9/12
- D.
8/12
Attempted by 19 students.
Show answer & explanation
Correct answer: B
Solution: Use inclusion–exclusion to compute P(A ∪ B).
Find P(A): P(A)=1−P(A')=1−1/3=2/3.
Find P(B): P(B)=1−P(B')=1−1/3=2/3.
Apply the union formula: P(A ∪ B)=P(A)+P(B)−P(A ∩ B)=2/3+2/3−1/2=4/3−1/2=5/6.
Therefore, P(A ∪ B)=5/6, which equals 10/12.