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BigFurryMonster

Guest

Statistics puzzle: probability of belonging to a group

Hello!

I'm struggling with the following puzzle:

I have a group of friends of which 60% is male.
I have a group of colleagues of which 70% is male.

Someone I know is both a friend and a colleague.

What is the chance that this person is male?

a) < 60 %
b) 60 %
c) between 60 en 70%
d) 70%
e) > 70%

(and why?)

Thanks for your help!
- BigFurryMonster

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,711

Re: Statistics puzzle: probability of belonging to a group

c) between 60 and 70%

because you are "mixing" the two probabilities:

the chance of being male is at least 60% (friends 60%, and colleagues 70% which is more than 60%), and at most 70% (colleagues 70%, and friends 60% which is less than 70%).

It won't be exactly 60%, because you are "mixing in" 70%, and it won't be 70% for the same reason.

We don't know the exact percentage, because we don't know the size of the groups.

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman