Three athlete A, B and C participate in a race competetion. probability of winning A and B is twice

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14.Probability

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Three athlete $A, B$ and $C$ participate in a race competetion. The probability of winning $A$ and $B$ is twice of winning $C$. Then the probability that the race win by $A$ or $B$, is

A

$\frac{2}{3}$

B

$\frac{1}{2}$

C

$\frac{4}{5}$

D

$\frac{1}{3}$

Solution

(c) $P(A) = P(B) = 2P(C),$

$P(A) + P(B) + P(C) = 1$

$ \Rightarrow P(C) = \frac{1}{5}$and $P(A) = P(B) = \frac{2}{5}$

Hence $P(A \cup B) = P(A) + P(B) = \frac{2}{5} + \frac{2}{5} = \frac{4}{5}.$

Standard 11

Mathematics

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