IMAT 2012 Q77 [Probability]

In a group of students, exactly {\frac {2}{5}} are male and exactly {\frac {1}{3}} study mathematics. The probability that a male student chosen at random from the group studies mathematics is p.

Which of the following is the range of possible values of p?

A. {\frac{1}{3}\le p \le 1}
B. { 0\le p \le \frac {5}{6}}
C. {\frac{1}{3} \le p \le \frac{2}{5}}
D. {\frac{2}{5} \le p \le \frac{5}{6}}
E. {0 \le p \le \frac {1}{3}}