Among the class of 100 students,
So a+b+c+d = 100
75 studied Botany,
So a+b = 75
55 studied Biology
So b+c = 55
and 40 students studied both of the subjects.
So b=40
Substituting 40 for b in b+c = 55
40+c = 55
c = 15
Substituting 40 for b in a+b = 75
a+40 = 75
a = 35
Substituting a=35, b=40, and c=15 in
a+b+c+d = 100
35+40+15+d = 100
90+d = 100
d = 10
A student is selected at random from this class what is the
probability that
i) student studied at least one subject
All but the 10. So that's 100-10 = 90 out of 100, so the probability
is 90/100 which reduces to 9/10
ii) student studied Botany but not Biology
That's the 35. So that's 35 out of 100, so the probability
is 35/100 which reduces to 7/20
iii) student studied Biology but not Botany.
That's the 15. So that's 15 out of 100, so the probability
is 15/100 which reduces to 3/20
iv) student studied none of the subjects
That's the 10 that aren't in either circle. So that's 10 out of 100,
so the probability is 10/100 which reduces to 1/10.
Edwin