Can I work out the probability that someone falls into two% categories

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martind13

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I'm not sure if it's possible to work out, I can't quite get my head around it, and that annoys me because I have an A at A level in maths and this seemingly simple problem is way beyond me. I want to know if there is a 92.9% chance you achieve something by belonging to group A and there's a 94% chance you achieve it by belonging to group B and it is possible to belong to both groups (but the value of how many people belong to each or both is unknown), what is the percentage chance of someone in both groups NOT achieving. For example 92.9% of people who do sports get an award and 94% of people who play a musical instrument get the same award what is the probability of someone who plays both sport and an instrument NOT achieving the award? I'm not sure if this makes any sense...and I'd appreciate if nobody just wrote the answer, I'd like to know what calculations you'd have to do and why so I can understand the answer. Is it possible to work this out? Thanks :)
 
martind13 said:
I'm not sure if it's possible to work out, I can't quite get my head around it, and that annoys me because I have an A at A level in maths and this seemingly simple problem is way beyond me. I want to know if there is a 92.9% chance you achieve something by belonging to group A and there's a 94% chance you achieve it by belonging to group B and it is possible to belong to both groups (but the value of how many people belong to each or both is unknown), what is the percentage chance of someone in both groups NOT achieving. For example 92.9% of people who do sports get an award and 94% of people who play a musical instrument get the same award what is the probability of someone who plays both sport and an instrument NOT achieving the award? I'm not sure if this makes any sense...and I'd appreciate if nobody just wrote the answer, I'd like to know what calculations you'd have to do and why so I can understand the answer. Is it possible to work this out? Thanks :)
Click to expand...

Can somebody get two awards - i.e. - one for music and one for sports?
 
It's one award...these are the percentages for getting it, can only get it once
 
martind13 said:
I'm not sure if it's possible to work out, I can't quite get my head around it, and that annoys me because I have an A at A level in maths and this seemingly simple problem is way beyond me. I want to know if there is a 92.9% chance you achieve something by belonging to group A and there's a 94% chance you achieve it by belonging to group B and it is possible to belong to both groups (but the value of how many people belong to each or both is unknown), what is the percentage chance of someone in both groups NOT achieving. For example 92.9% of people who do sports get an award and 94% of people who play a musical instrument get the same award what is the probability of someone who plays both sport and an instrument NOT achieving the award? I'm not sure if this makes any sense...and I'd appreciate if nobody just wrote the answer, I'd like to know what calculations you'd have to do and why so I can understand the answer. Is it possible to work this out? Thanks :)
Click to expand...
P(award | A) = 0.929,....P(no award | A) = 0.071
P(award | B) = 0.94,......P(no award | B) = 0.06

In the absence of any knowledge about joint membership, you have to assume that memberships in A and B are statistically independent, that is
P(A) = P(A | B) = P(A | notB)
P(B) = P(B | A) = P(B | notA)
Does that get you any farther? Can you use Bayes's theorem somehow?
 
You say "there is a 92.9% chance you achieve something by belonging to group A and there's a 94% chance you achieve it by belonging to group B and it is possible to belong to both groups"

So what is the probability of achieving it if you belong to both groups?
 
HallsofIvy said:
You say "there is a 92.9% chance you achieve something by belonging to group A and there's a 94% chance you achieve it by belonging to group B and it is possible to belong to both groups"

So what is the probability of achieving it if you belong to both groups?
Click to expand...

That's what I'm trying to find out...well what's the possibility of not achieving it if you belong to both... so the inverse but basically that's what I'm trying to figure out. I guess that it's not possible to work it out without knowing more information
 
Just knowing the probability of belonging to one group or the other is NOT enough to tell you the probability of belonging to BOTH groups. That was why I asked. You need that information separately.

For example, suppose that, of 100 people, 50 belonged to group A only, 30 belonged to group B only, 20 belonged to neither, and none belonged to both.

For a different example, suppose that, of 100 people, 30 belonged to group A only, 10 belonged to group
B only, 20 belonged to neither, and 20 belonged to both.

In both cases we have "50 belonged to group A and 30 belonged to group B" but different numbers of people belonged to both.
 
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