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Probability

For a post th...

Question

For a post three persons A, B and C appear in the interview. The probability of A being selected is twice that of B and the probability of B being selected is thrice that of C, what are the individual probabilities of A, B, C being selected?

P (E_{1}) = \frac{3}{5}

P (E_{2}) = \frac{1}{10}

P (E_{3}) = \frac{3}{10}

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P (E_{1}) = \frac{3}{10}

P (E_{2}) = \frac{3}{5}

P (E_{3}) = \frac{1}{10}

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P (E_{1}) = \frac{3}{10}

P (E_{2}) = \frac{3}{10}

P (E_{3}) = \frac{1}{10}

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P (E_{1}) = \frac{3}{5}

P (E_{2}) = \frac{3}{10}

P (E_{3}) = \frac{1}{10}

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Solution

The correct option is D $P (E_{1}) = \frac{3}{5}$ , $P (E_{2}) = \frac{3}{10}$ , $P (E_{3}) = \frac{1}{10}$
Let the probability of C being selected be $k$ $\Rightarrow$ probability of B being selected $= 3 k$ $\Rightarrow$ probability of A being selected $= 2 (3 k) = 6 k$
Hence, $P (E_{1}) = \frac{6 k}{6 k + 3 k + k} = \frac{6}{10} = \frac{3}{5}$

$P (E_{2}) = \frac{3 k}{6 k + 3 k + k} = \frac{3}{10}$

$P (E_{3}) = \frac{k}{6 k + 3 k + k} = \frac{1}{10}$

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