I will appreciate it if someone can explain why the maximum P can be 5/6.

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This is conditional probability.

We must make a table like this one:

They are asking what is the probability its a MALE who studies MATHS. So 1/3 is the maximum n. of students who study maths divided by the total number of males (2/5) gives us 5/6. The minimum is of course 0.

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