Three friends Ravi, Sonia and Vishal appeared in a interview for three vacancies in the same post. The probability of Ravi's selection is(1/8) , Sonia's selection is (2/7) and Vishal's selection is (1/5). What is the probability that only one of them is selected?
117/ 237
111/280
3/27
None of these
Answer :111/280
Solution (Fast Approach)
Probability of selection of only Ravi: (Probability of selection of Ravi) and (Probability of not selection of Sonia) and (Probability of not selection of Vishal)
=> (1/8)*(1-2/7)*(1-1/5)
=>Solving above we get 1/14
Now Probability of selection of only Sonia: (Probability of not selection of Ravi) and (Probability of selection of Sonia) and (Probability of not selection of Vishal)
=> (1-1/8)*(2/7)*(1-1/5)
=>Solving above we get 1/5
Now Probability of selection of only Vishal: (Probability of not selection of Ravi) and (Probability of not selection of Sonia) and (Probability of selection of Vishal)
=> (1-1/8)*(1-2/7)*(1/5)
=>Solving above we get 1/8
Hence Probability of anyone of them and not the others two is = 1/14 + 1/5 + 1/8 = 111/280
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