Ajay and his wife Reshmi appear in an interview for two vaccancies in the same post. The Probability of Ajay's selection is 1/7 and that of his wife Reshmi's selection is 1/5. What is the probability that only one of them will be selected?
Solution
Correct Answer: Option C
P( only one of them will be selected) = p[(E and not F) or (F and not E)]
= \(P\left[\left(E\cap F\right)\cup\left(F\cap E\right)\right]\)
= \(P\left(E\right)P\left(F\right)+P\left(F\right)P\left(E\right)\)
= \(\frac17\times\frac45+\frac15\times\frac67=\frac27\)
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