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.

Question

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

TestHub · Accepted Answer

Let Q → event that 'PRANAM' is selected. S → event that 'SALAAM' is selected H → event that 'HELLO' is selected. E → event that the letter chosen is A or L . P ( Q / E ) = P ( Q ) P ( E / Q ) + P ( S ) P ( E / S ) + P ( H ) P ( E / H ) P ( Q ) P ( E / Q ) ​ = 3 1 ​ × 6 2 ​ + 3 1 ​ × 6 4 ​ + 3 1 ​ × 5 2 ​ 3 1 ​ × 6 2 ​ ​ = 21 5 ​

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