If A and B are mutually exclusive events, then following probability of the events are given below:
(A) \(P(A)=0.4\), \(P(B)=0.4\) and \(P(A\cup B)=0.8\)
(B) \(P(A)=0.3\), \(P(B)=0.6\) and \(P(A\cup B)=0.9\)
(C) \(P(A)=0.3\), \(P(B)=0.3\) and \(P(A\cup B)=0.6\)
(D) \(P(A)=0.1\), \(P(B)=0.1\) and \(P(A\cup B)=0.2\)
which of the following options is correct?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A), (B), (C) and (D)
Mutually exclusive events cannot happen together, so \(P(A\cap B)=0\) and the addition rule becomes \(P(A\cup B)=P(A)+P(B)\). Each set of values is tested against this rule (every value also lies between 0 and 1).
(A) \(P(A)=0.4\), \(P(B)=0.4\) and \(P(A\cup B)=0.8\) Correct. \(0.4+0.4=0.8\), as given.
(B) \(P(A)=0.3\), \(P(B)=0.6\) and \(P(A\cup B)=0.9\) Correct. \(0.3+0.6=0.9\), as given.
(C) \(P(A)=0.3\), \(P(B)=0.3\) and \(P(A\cup B)=0.6\) Correct. \(0.3+0.3=0.6\), as given.
(D) \(P(A)=0.1\), \(P(B)=0.1\) and \(P(A\cup B)=0.2\) Correct. \(0.1+0.1=0.2\), as given.