Question

A sample of 50 students was surveyed on whether they owned an iPod or a mobile
phone. The results showed that 38 per cent of the students owned both. Sixty
per cent of the students owned a mobile phone, and there were four students who had an iPod only. What percentage of students did not own a mobile phone or an iPod?

Answer 1

U = Universal set, A = having a phone, B = having an ipod

n(U) = 50
n(A∩B) = 0.38*50 = 19
n(A) = 0.6*50 = 30

n(B-A) = n(B) - n(A∩B) = 4
=> n(B) = 4 + n(A∩B) = 4 + 19 = 23

Now,

n(A∪B) = n(A) + n(B) - n(A∩B)
= 23 + 30 - 19
= 34

Students who did not own either = n(U) - n(A∪B)
= 50 - 34 = 16

Answer 2

easy to understand, thanks.

Answer 3

also, in the statement - "there were four students who had an iPod 'only,'" the 'only' signifies that you are to add 19 to 4 and not add 19 with mobile as well?