Consider the following three words (written in capital letters): ‘PRANAM’,’SALAAM’ and ‘HELLO’ One of the three words is chosen at random and a letter from it is drawn. The letter is found to be ‘A’ or ‘L’ then the probability that it has come from the word ‘PRANAM’ is

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$\frac{5}{21}$

$\frac{2}{5}$

$\frac{14}{21}$

$\frac{1}{3}$

answer is A.

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Detailed Solution

Let $Q \to$ event that ‘PRANAM’ selected $S \to$ event that ‘SALAAM’ is selected $H \to$ event that ‘HELLO’ is selected $E \to$ event that the letter chosen is A or L

$P (\frac{Q}{E}) = \frac{P (Q) P (E / Q)}{P (Q) P (E / Q) + P (S) P (E / S) + P (H) P (E / H)} = \frac{\frac{1}{3} \times \frac{2}{6}}{\frac{1}{3} \times \frac{2}{6} + \frac{1}{3} \times \frac{4}{6} + \frac{1}{3} \times \frac{2}{5}} = \frac{5}{21}$

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