A survey of 40 students showed that 23 students study Mathematics, 5 study Mathematics and Physics, 8 study Chemistry and Mathematics, 5 study Physics and Chemistry and 3 study all the three subjects. The number of students who study Physics only is twice the number who study Chemistry only.
(a) Find the number of students who study:
(i) only Physics.
(ii) only one subject
b) What is the probability that a student selected at random studies exactly 2 subjects?
Explanation
Let \(\mu\) = 40 n(M) = 23, n(M \(\cup\) P) = 5, n(M \(\cup\) C) = 8, n(P \(\cup\) C) = 5, n(M \(\cup\) P \(\cup\) C) = 3, n(C) only = x and n(P) only = 2x
(a)(i) We have 13 + 2 + 3 + 5 + x + 2 + 2x = 40 and solving for x will yield x = 5, so that the number of students that studied only Physics = 2(5) = 10
(a)(ii) The number of students that studied only one subject is 13 + 10 + 5 = 28
(b) The probability that a student selected at random studies exactly two subjects = \(\frac{5 + 2 + 2}{40} = \frac{9}{48}\) or 0.225