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?

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

easy to understand, thanks.

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?

To find the percentage of students who did not own a mobile phone or an iPod, we need to subtract the total percentage of students who owned both, owned a mobile phone only, and owned an iPod only from 100%.

Let's break down the given information:
- 38% of the students owned both an iPod and a mobile phone.
- 60% of the students owned a mobile phone.
- 4 students had an iPod only.

First, let's calculate the percentage of students who owned a mobile phone or an iPod.

Percentage of students who owned a mobile phone or an iPod:
= Percentage of students who owned both + Percentage of students who owned a mobile phone only + Percentage of students who owned an iPod only.

The percentage of students who owned both is given as 38%.

The percentage of students who owned a mobile phone only can be calculated as follows:
= 60% (students who owned a mobile phone) - 38% (students who owned both)
= 22%.

The number of students who owned an iPod only is given as 4.

Now, to calculate the percentage of students who did not own a mobile phone or an iPod:

Percentage of students who did not own a mobile phone or an iPod:
= 100% - Percentage of students who owned a mobile phone or an iPod.

Percentage of students who owned a mobile phone or an iPod:
= Percentage of students who owned both + Percentage of students who owned a mobile phone only + Percentage of students who owned an iPod only.
= 38% + 22% + 4%
= 64%.

Therefore, the percentage of students who did not own a mobile phone or an iPod
= 100% - 64%
= 36%.