Math Destroyer question

[DK17]

Fellow SDN'ers, I need clarity on this question.

Half the population of Green Village is vegetarians, and 35% ride bicycles. If 20% are both vegetarian and ride bicycles, what is the probability that a person chosen at random from Green Village is either a vegetarian or rides a bicycle.

A. 95%
B. 65%
C. 12%
D. 83%
E. 24%

Solution in the back says its B, but if I think of it, why is it simply not: 50/100 + 35/100 = 85/100 or 85% either a vegetarian or rides a bicycle? Why does the 20% even matter? Sorry if this is a stupid question, just been bothering me and lingering in the back of my mind, need an answer -_-.

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[Roy Williams]

Standard prob rules.

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Therefore,
P(veg ∪ bik) = P(veg) + P(bik) - P(veg ∩ bik) = .5 + .35 - .2 = .65 (B)

 

[Trave_]

Since 25% of people do both, then that's an overlap that needs to be removed or else you're counting the same people twice. (50-20) + 35 (or (35-20) +50) would be a better way of looking at it.

 

[Roy Williams]

Since 25% of people do both, then that's an overlap that needs to be removed or else you're counting the same people twice. (50-20) + 35 (or (35-20) +50) would be a better way of looking at it.

This is a problem where you don't even have to try to reason it out and possibly confuse yourself. I know a lot of people have trouble with the ven diagrams. If you can just remember 1 or 2 formulas then you'll be set.

Probability Rules - this link details some of them

 

[DK17]

Ahhhh, better understood by, they want either/or, not including both. You guys are awesome, it seems like I didn't read the question thoroughly enough. Thanks for clearing that up guys [: