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In a competition A, B and C are participating. The probability that A wins is twice that of B, the probability that B wins is twice that of C. Then the probability that A loses is (A, B and C are mutually exclusive and exhaustive events)

In a competition A, B and C are participating. The probability that A wins is twice that of B, the probability that B wins is twice that of C. Then the probability that A loses is (A, B and C are mutually exclusive and exhaustive events) Correct Answer 3/7

Concept:

Mutually Exhaustive Event:

  • A set of events is collectively exhaustive where at least one of the events must occur.
  • Example, when rolling a six-sided die, the outcomes 1, 2, 3, 4, 5, and 6 are collectively exhaustive, because they encompass the entire range of possible outcomes.
  • A, B and C are mutually exclusive and exhaustive events.
  • P (A ∪ B ∪ C) = P (A) + P (B) + P (C)

 

Calculation:

Given: A, B and C are mutually exclusive and exhaustive events.

P (A) = 2 × P (B)

∴ P (B) = P (A)/2

P (B) = 2 × P(C)

⇒ P(C) = P (B)/2

We know that P (B) = P (A)/2

∴ P(C) = P (B)/4

A, B and C are mutually exclusive and exhaustive events.

∴ P (A ∪ B ∪ C) = P (A) + P (B) + P (C)

⇒ 1 = P (A) + P (A)/2 + P (A)/4 = (4/7) × P (A)

∴ P (A) = 4/7

Then the probability that A loses is: 1 - P (A) = 1 - 4/7 = 3/7

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