duh? 50%

If we assume that 20%(100% - (40%+30%+10%)) don''t like any of the music, then 40% like alternative who don''t like rap. ''Cause there are 20% who don''t like any, and there are 30% who like rap, and 10% who like both, that''s 60% who like rap or nothing. That just leaves 40% who likes alternative and not rap.

But perhaps the fraction of people you are looking for excludes the left over 20%...... I may be misunderstanding the question.

30%

> Suppose 40% of People like Alternative Music, 30% like Rap and 10% like both.
>
> What percent of people like Alternative but not Rap?

metalwood''s right.

Easiest to explain using a picture. Standard intersection problem. Imagine two circles, one red, one blue, partially overlapping; one represents Alternative, one represents Rap.

In the section which is red only (rap), 20% reside.
In the section which is blue only (alternative), 30% reside.
In the section which is purple (intersection; rap and alternative), 10% reside. Outside the circles 40% reside.

Clearly; the total % who like Alternative is 30% (20% + 10% who like both). The total % who like rap is 40% (30% + 10% who like both). The middle bit is 10%. This is consistant with what you stated.

Ie. The Percentage for like alternative, but not rap are 30%.

I have no idea where all these weird numbers are coming from.

25%

Here''s what we know:

40% - Alternative (and maybe rap too)
30% - Rap (and maybe alternative too)
10% - Both

If we subtract the "Both" population from the "Alternative" population we are left with those who like alternative but not rap. Hence, the population that likes alternative but not rap is 40% - 10% = 30%.

In other words: Two squares, A and B, intersect each other. The area of square A is 40 cm2. The area of square B is 30 cm2. The area occupied by both squares is 10 cm2. What area of square A is not shared by square B?

Pretty clearly, it''s 40 cm2 minus 10 cm2, or 30 cm2. Use that metaphor to visualize this problem.

metalwood and Shadow Mint were right.

Just a quick explanation (for Wojtos benefit) of all of these ''circle and square'' answers:

What these posters are referring to is a Venn Diagram, which is a nice visual method of interpreting probabilities.

A Venn Diagram can be constructed for this problem by drawing a rectangle. Within the rectangle, draw two circles that slightly overlap each other (but not the sides of the rectangle. One circle represents 30% of the area of the rectangle and the other represents 40% of the area of the rectangle. Where the two circles overlap, this should be sized to represent 10% of the rectangle.

Now you have represented the various sets that your problem identifies. The 40% circle represents the proportion of the population that like Alternative music. The 30% circle represents the proportion of the population that likes Rap music. The overlap is the proportion of the population that likes both types of music. Clearly the area of the rectangle represents the size of the population.

Now it is easy to deduce by visual means that the area of the Alternative music set that DOESN''T overlap with the Rap music set is 0.4 - 0.1 = 0.3. Hence 30% of the population like Alternative music but not Rap music.

I hope this makes the former explanations a little clearer for you and helps you to understand Venn Diagrams a little better.

Regards,

Timkin