A and B are two mutually exclusive and exhaustive events with P(B) = 3P(A). What is the value of P (bar(B)) ? -Maths 9th

A and B are two mutually exclusive and exhaustive events with P(B) = 3P(A). What is the value of P (bar(B)) ? -Maths 9th
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1 Answer

Answer :

(c) 43 : 34Given, odds against A = 8 : 3⇒ P(not A) = \(rac{8}{8+3}\) = \(rac{8}{11}\) ⇒ P(A happens) = \(rac{3}{11}\)Odds against B = 5 : 2⇒ P(not B) = \(rac{5}{5+2}\) = \(rac{5}{7}\) ⇒ P(B happens) = \(rac{2}{7}\)As out of A, B and C, one and only one can happen, so P(A) + P(B) + P(C) = 1 P(C) = 1 – (P(A) + P(B))= 1 - \(\bigg(\)\(rac{3}{11}\) + \(rac{2}{7}\)\(\bigg)\) = 1 - \(\bigg(rac{21+22}{77}\bigg)\) = 1 - \(rac{43}{77}\) = \(rac{34}{77}\)P(not C) = 1 - \(rac{34}{77}\) = \(rac{43}{77}\)odds against C = \(rac{P(not\,c)}{P(c)}\) = \(rac{rac{43}{77}}{rac{34}{77}}\) = 43 : 34.
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