Question
Download Solution PDFLet A and B are two mutually exclusive events with
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Mutually exclusive events:
- Two events are said to be mutually exclusive if they cannot happen at the same time.
- Example: if we toss a coin, either heads or tails might turn up, but not heads and tails at the same time.
- If A and B are mutually exclusive events then, P (A∩B) =0 and P (A ∪ B) = P (A) + P (B)
Complement of an event:
- The complement of an event is the subset of outcomes in the sample space that are not in the event. A complement is itself an event.
- The probability of the complement of an event is one minus the probability of the event.
- P (A’) or P (Ac) or
= 1 - P (A) Where (A) be probability of Event A and P (A’) or P (Ac) or be probability of the complement of Event A
Calculation:
Given: P(A) = 1/3 and P(B) = 1/4
As we know that
Now, P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
A and B are two mutually exclusive events so P(A ∩ B) = 0
∴ P(A ∪ B) = P(A) + P(B) = (1/3) + (1/4) = 7/12
Now,
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