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}}


The easiest claim we can make when we first read this question is the fact that none of the males could have been selected. This means the range of possible values for p must begin at 0.