Answer to Question #232047 in Statistics and Probability for AmyCole

Question

Out of a class of 120 students, 30 students do not take any of Physics, Chemistry, or Biology. 15 of them take only Physics, 25 of them take Chemistry and Biology but not Physics, 20 of them take Physics and Biology but not Chemistry, 10 of them take all the three of Physics, Chemistry, and Biology. A total of 45 of them take Chemistry.

(i) How many of the students take Physics and Chemistry but not Biology.

(ii) How many students take only Biology?

(iii) What is the total number of students taking Biology?

(iv) If a student is chosen at random, from those who take neither Chemistry nor Biology, what is the probability that he/she does not take Physics either.

(v) If one of the students who take at least two of the three courses is chosen at random, what is the probability that he/she takes all three courses.