Question

In a class of 60 students, 30 opted for Mathematics, 32 opted for Biology and 24 opted for both Mathematics and Biology. If one of these students is selected at random, find the probability that: 

(i) The student opted for Mathematics or Biology.
(ii) The student has opted neither Mathematics nor Biology.
(iii) The student has opted in Mathematics but not Biology.

Answer 1

U = 60
n(M) = 30
n(B) = 32
n(M ∩ B) = 24
n(M ∪ B) = n(M) + n(B) – n(M ∩ B) = 30 + 32 – 24 = 38
n(M ∪ B)’ = n(∪) – n(M ∪ B) = 60 – 38 = 22
Only Mathematics = n(M) – n(M ∩ B) = 30 – 24 = 6

(i) P(student opted for Mathematics or Biology) =`24/60 = 2/5` 
(ii) P(student opted neither Mathematics nor Biology) `=22/60 = 11/30`  
(iii) P(student opted Mathematics but not Biology) `=6/60 = 1/10`