ProbabilityHard
Question
Before a race the chance of three runners A, B & C were estimated to be proportional to 5, 3 & 2 respectively but during the race A meets with an accident which reduces his chance to 1/3. If the respective chances of B and C are P(B) and P(C) then -
Options
A.P(B) = 2/5
B.P(C) = 4/15
C.P(C) = 2/5
D.P(B) = 4/15
Solution
Ratio of their probabilities are 5 : 3 : 2
⇒ 5x + 3x + 2x = 1 ⇒ x =
their respective probabilities of A, B & C will be
=
Now After A′s accident
- t = 
⇒ t =
probability get reduced
which will be shared between B & C
⇒ 3y + 2y =
⇒ y = 
⇒ Probability of C =
Probability of B =
⇒ 5x + 3x + 2x = 1 ⇒ x =
their respective probabilities of A, B & C will be
=
Now After A′s accident
- t = ⇒ t =
probability get reducedwhich will be shared between B & C
⇒ 3y + 2y =
⇒ y = ⇒ Probability of C =
Probability of B =
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