Problem Solving

Hi all ,

I have come across the below problem in Probability and need your help to solve the same .

Problem
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Kamal and Monica appeared for an interview for two vacancies . The probability of Kamal's selection is 1/3 and that of Monica's rejection is 4/5 . Find the probability that only one of them will be selected .

Solution suggested by the book :
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Let K be the event that Kamal will be selected and M the event that Monica will be selected .
Then P(K) = 1/3 and P(M^c) = 4/5
Therefore P(M) = 1 - P(M^c) = 1-4/5 = 1/5
and P(K^c) = 1-1/3 = 2/3

Only one of them will be selected if either i.) Kamal is selected and Monica is not selected or ii.) Monica is selected and Kamal is not

In case i.) Probability = 1/3 * 4/5 = 4/15
In case ii.) Probability = 2/3 * 1/5 = 2/15

Hence the required probability , that one of them will be selected is
4/15 + 2/15 = 6/15= 2/5

My approach
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Required probability = P(K) + P(M) -P(K).P(M)
= 1/3 + 1/5 - 1/15
= 7/15

Could someone tell me where I am making a mistake .