Here is a puzzle for you:
In a group of people, 40% are men and the rest are women. It is also given that in this group 40% of the men and 10% of the women are obese.
What is the probability that an obese person in the group is a man?
When you find the solution, post it as a comment or send it to me. The solution will be explained in a later post.
P(m) = 0.40, P(w) = 0.60
P(o|m) = 0.40, P(o|w) = 0.10
P(o) = P(m) * P(o|m) + P(w) * P(o|w) = 0.22
Bayes’ Rule
P(m|o)
= P(o|m) P(m) / P(o)
= 0.40 * 0.40 / 0.22
= 72.3 %
oops, 72.7 %, I hope.
72.7
72.727272727272727272727272727273
I think so…
72.73, but apparently I am not the FGITW.
16/22 I believe.
Am I right?
62.5?
A nice little puzzle. The answer 16/22 (or 72.73%) is correct. Assume you have 100 people, 40 men and 60 women. That means 16 of the men (40% of 40) and 6 of the women (10% of 60) are obese, for a total of 22 obese people. If you randomly select one obese person, the odds are 16/22 that they are male.
22(obese)=16(male) + 6(female)
16(male)/22(obese) = whatever .
is the answer I think.
There are 16 obese man and 6 obese women in every 100 people.
Hence, probability that an obese person in the group is a man will be = 16/(16+6) = 72.73%
@ Andy – Nice, thanks to your solve I remembered my High school mathematics
Its a standard application of Bayes Theorem.
P(man|obese) = (0.4*0.4)/(0.4*0.4 + 0.6*.1)
= 0.727
well I think its : 2/5
Thant is 2 out of every 5 male is obese…….
Lets us assume there are 100 people
therefore 40 men are there
40% of 40 is 16
thus, 16 men out of 40 are obese
therefore the probability is 16/40= 2/16
sorry in the last line I meant 16/40=2/5
Just wondered if the answer to this puzzle was ever given?
@Flick,
This is one of those questions where your intuitions may fail you in getting to the correct answer. Regardless, since many of the readers of this blog are geeks, most of them (who commented) got the answer correct. So I thought there was no need for a follow up post.
I think the search engines should consider this fact before crawling my server to death.
A couple has two children, and one of them is a girl.
What is the probability that the other child is a male?
2/3 ?
Intuition works
I Think the probably of be a man is 16% , mmmhh but I didn’t aprobe statistics jejee
Como quitar las estrias