Venn diagram problem

Cuttlefish

Hi,
I am doing some junior cert project maths revision on chapter 10 of the text and test 2 book and am kind of stuck on a Venn diagram question on page 203.

"in a group of 25 students, 18 study maths, 12 study science and 5 study neither maths or science.
Illustrate this information on a venn diagram.
If a student is selected at random, what is the probability that the student studies
1. Maths only
2. Science only
3. Maths or Science or both
4. Both maths and science

I know that 5 are neither maths or science so they are outside the venn diagram but how do I determine of the figures 18 and 12 that they study maths only, science only or both?

Bazinga_N

Cuttlefish wrote: »

Hi,
I am doing some junior cert project maths revision on chapter 10 of the text and test 2 book and am kind of stuck on a Venn diagram question on page 203.

"in a group of 25 students, 18 study maths, 12 study science and 5 study neither maths or science.
Illustrate this information on a venn diagram.
If a student is selected at random, what is the probability that the student studies
1. Maths only
2. Science only
3. Maths or Science or both
4. Both maths and science

I know that 5 are neither maths or science so they are outside the venn diagram but how do I determine of the figures 18 and 12 that they study maths only, science only or both?

From all the info given you add them together to get 35 (18+12+5), but the question says the group has 25 students. So if 5 study neither, you're left with 30 even though you should only have 20 students left. So 30-20 = 10. This ten is the amount of students who study both science and math. Therefore the number of students who study science only is 2 (12-10) and the amount of students only studying maths only is 8 (18-10).

To make sure you're correct add the info you got together (5+10+2+8) to get 25, which is how many students you should have.