Thread: what is the chance of this happening

1. [RESOLVED]what is the chance of this happening

I'm stuck on this question
Suppose that 40% of visitors to a city visit the mountains, 70% visit the parks and 20% visit both sites. One visitor is randomly slected. What is the probability that the visitor visits at least 1 of the 2 sites?

I tried adding 40%+70%+20% but that's more than 100%

2. Originally Posted by Jskid
I'm stuck on this question
Suppose that 40% of visitors to a city visit the mountains, 70% visit the parks and 20% visit both sites. One visitor is randomly slected. What is the probability that the visitor visits at least 1 of the 2 sites?

I tried adding 40%+70%+20% but that's more than 100%
Think in terms of sets/Venn diagrams...

3. Is it 40%+70%-20% because the overlapping portion is allready counted in the 40% and 70%?

4. Originally Posted by Jskid
Is it 40%+70%-20% because the overlapping portion is allready counted in the 40% and 70%?
Yes. What you did was count first with duplicates, and then subtract the duplicates to get the correct answer. (Well done!) Another (longer) way to think of it is:

40% visit mountains
70% visit parks
20% visit both

If 40% visit mountains and 20% visit both, then 20% visit ONLY mountains.

If 70% visit parks and 20% visit both, then 50% visit ONLY parks.

So (only mountains) + (both mountains and parks) + (only parks) = 20% + 20% + 50% = 90%.

By the way, the way you dealt with duplicates is a special case of the more general inclusion–exclusion principle.