Kamal and Monica appeared for an interview for two vacancies. The probability of Kamal’s selection is and that of Monica’s selection is Find the probability that only one of them will be selected. - Wired Faculty

Question

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Kamal and Monica appeared for an interview for two vacancies. The probability of Kamal’s selection is $1 third$ and that of Monica’s selection is $4 over 5.$ Find the probability that only one of them will be selected.

Solution

Let A denote the event ‘Kamal is selected’ and B denote the event ‘Monica is selected’.

therefore space space space straight P left parenthesis straight A right parenthesis space equals space 1 third comma space space straight P left parenthesis straight B right parenthesis space equals space 4 over 5 therefore space space straight P left parenthesis straight A with bar on top right parenthesis space equals space 1 minus straight P left parenthesis straight A right parenthesis space equals space 1 minus 1 third space equals 2 over 3 space space space space space straight P open parentheses straight B with bar on top close parentheses space equals space 1 minus straight P left parenthesis straight B right parenthesis space equals space 1 minus 4 over 5 space equals 1 fifth

P(only one of them is selected)

equals space straight P left parenthesis apostrophe straight A space and space straight B with bar on top apostrophe space space space or space space space apostrophe straight A with bar on top space and space straight B apostrophe right parenthesis space equals straight P left parenthesis straight A space and space straight B with bar on top right parenthesis space plus space straight P left parenthesis straight A with bar on top space and space straight B right parenthesis space equals space straight P left parenthesis straight A right parenthesis. space straight P left parenthesis straight B with bar on top right parenthesis space plus space straight P left parenthesis straight A with bar on top right parenthesis. space straight P left parenthesis straight B right parenthesis space equals space 1 third cross times 1 fifth plus 2 over 3 cross times 4 over 5 space equals 1 over 15 plus 8 over 15 space equals 9 over 15 space equals 3 over 5

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Probability

Kamal and Monica appeared for an interview for two vacancies. The probability of Kamal’s selection is $1 third$ and that of Monica’s selection is $4 over 5.$ Find the probability that only one of them will be selected.

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