Let A, B and C be three mutually exclusive and exhaustive events associated with a random experiment. If P (B) = 1.5 P (A) and P (C) = 0.5 P (B), then P (A) is equal to
4/13
Concept:
- A, B, and C are mutually exclusive and collectively exhaustive events related to a random experiment.
- P (A ∪ B ∪ C) = P (A) + P (B) + P (C)
- If A ∪ B ∪ C = S = sample space ⇔ P (A ∪ B ∪ C) = 1
Calculation:
Given:
P (B) = 1.5 P (A) and P (C) = 0.5 P (B) and
A, B, and C are mutually exclusive and collectively exhaustive events related to a random experiment.
⇒ P (A ∪ B ∪ C) = 1
⇒ P (A) + P (B) + P (C) = 1
⇒ P (A) + 1.5 P (A) + 0.5 P (B) = 1
⇒ 2.5 P (A) + 0.5 × 1.5 P (A) = 1
⇒ 2.5 P (A) + 0.75 P (A) = 1
⇒ 3.25 P (A) = 1
⇒ P (A) = 1/3.25 = 4/13
∴ Option 2 is correct.
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