Prof. L decides to assign final grades in CS 333 by ignoring all the work the students have done and instead using the following probabilistic method: each student independently will be assigned an A with probability , a B with probability 3, a C with probability 1/ 2 , and an F with probability (1/ 2) - 4. When the quarter is over, you discover that only 2 students got an A, 10 got a B, 60 got a C, and 40 got an F.

Find the maximum likelihood estimate for the parameter that Prof. L used. Give an exact answer as a simplified fraction.

Please, show steps in detail withexplanations so that I can walk through.