To find the probability that only one of the two persons, A and B, is selected, we need to consider the individual probabilities of their selection and then calculate the probability of the desired outcome.

Given:
- Probability of A's selection = 1/5
- Probability of B's selection = 2/7


To calculate the probability that only one person is selected, we need to consider two cases:
1. A is selected and B is not selected.
2. B is selected and A is not selected.


The probability of A being selected is 1/5.
The probability of B not being selected is 1 - (2/7) = 5/7 (since the total probability is 1).

To calculate the probability of both events happening, we multiply their individual probabilities:
Probability of A being selected and B not being selected = (1/5) * (5/7) = 1/7


The probability of B being selected is 2/7.
The probability of A not being selected is 1 - (1/5) = 4/5.

To calculate the probability of both events happening, we multiply their individual probabilities:
Probability of B being selected and A not being selected = (2/7) * (4/5) = 8/35


To find the probability that only one person is selected, we need to add the probabilities of the two cases:
Probability of only one person being selected = Probability of A being selected and B not being selected + Probability of B being selected and A not being selected
= 1/7 + 8/35
= 5/35 + 8/35
= 13/35


The probability that only one person is selected is 13/35. This means that in the given scenario, there is a 13/35 chance that either person A or person B will be selected, but not both.