Probability problem!

[FROGGBUSTER]

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Half of a certain population is weightlifters and 35% are powerlifters. If 20% are both weightlifters and powerlifters, what is the probability that a person chosen at random is either a powerlifter or a weightlifter?

I found the answer to be 15+30=45% (either but not both right?). But the answer says it should be 15+30+20=65%, which includes both.

What do you guys think?

 

[herkulease]

I do it like this

50% weightlifters + 35% powerlifters - 20% that is both will get 65% of population that is either a weightlifter or powerlifter.

 

[HannibalLecter]

I do it like this

50% weightlifters + 35% powerlifters - 20% that is both will get 65% of population that is either a weightlifter or powerlifter.

I agree with Herkulease

Thats how its stated in the math destroyer, good job dude

 

[FROGGBUSTER]

Thanks guys, but can someone explain why the way I did it was incorrect?

 

[Waldo2012]

Thanks guys, but can someone explain why the way I did it was incorrect?

Where did you get 15 and 20 from? You include the percent that is both in your end equation. I am confused on why what you are doing makes sense. Just think of it as the way already explained.

 

[HannibalLecter]

Where did you get 15 and 20 from? You include the percent that is both in your end equation. I am confused on why what you are doing makes sense. Just think of it as the way already explained.

He's subtracting the probability for both PL and WL from each of the probability of PL and WL so hes left for the probability of PL alone and WL alone.

The way you are doing it Frogger is that you are counting only PL alone and WL alone but in this probability it states its either a PL or a WL which also includes both of them together. If you took out that part of the population that does both then you get the wrong probability because you have to count those people who are doing both. You have to include that part of the population in the probability but just once. Hope this explains it. But probably the best way to do it is like how it is stated above.

 

[FROGGBUSTER]

He's subtracting the probability for both PL and WL from each of the probability of PL and WL so hes left for the probability of PL alone and WL alone.

The way you are doing it Frogger is that you are counting only PL alone and WL alone but in this probability it states its either a PL or a WL which also includes both of them together. If you took out that part of the population that does both then you get the wrong probability because you have to count those people who are doing both. You have to include that part of the population in the probability but just once. Hope this explains it. But probably the best way to do it is like how it is stated above.

I see, so when the question says "either a powerlifter or weightlifter," someone who is both does count then?

 

[HannibalLecter]

I see, so when the question says "either a powerlifter or weightlifter," someone who is both does count then?

Yes