Question

For the two mutually exclusive events \(A\) and \(B\), which of the following are correct? A. \(P(A\cup B)=P(A)+P(B)\)
B. \(P(A\cap B)=0\)
C. \(P(A\cap B)=P(A)\cdot P(B)\)
D. \(P(A\cap B)=P(A/B)P(B)\)
E. \(P(A)=P(A/B)P(B)\)

• A. A, C and E only
• B. A, B and D only
• C. A and D only
• D. B, C only

Hint:

For mutually exclusive events, \(P(A\cap B)=0\) and \(P(A\cup B)=P(A)+P(B)\).

Answer 1

The Correct Option is B

Concept:
Two events are mutually exclusive if they cannot occur together. \[ A\cap B=\phi \]

Step 1: Check A.
For mutually exclusive events: \[ P(A\cup B)=P(A)+P(B) \] So, A is correct.

Step 2: Check B.
Since events are mutually exclusive: \[ P(A\cap B)=0 \] So, B is correct.

Step 3: Check C.
The formula: \[ P(A\cap B)=P(A)P(B) \] is for independent events, not mutually exclusive events in general. So, C is incorrect.

Step 4: Check D.
By multiplication theorem: \[ P(A\cap B)=P(A/B)P(B) \] So, D is correct as a general probability identity. Thus: \[ A,B,D \] \[ \therefore \text{Correct Answer is (B)} \]