A quick little puzzle

Jan 27 2010

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.

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13 responses so far

  1. # AndyHon 27 Jan 2010 at 2:39 pm

    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 %

  2. # AndyHon 27 Jan 2010 at 2:44 pm

    oops, 72.7 %, I hope.

  3. # Ragsamon 27 Jan 2010 at 2:56 pm

    72.7

  4. # Deepakon 27 Jan 2010 at 3:02 pm

    72.727272727272727272727272727273

    I think so… :)

  5. # Amarghoshon 27 Jan 2010 at 5:00 pm

    72.73, but apparently I am not the FGITW.

  6. # charliesomeon 27 Jan 2010 at 5:21 pm

    16/22 I believe.

    Am I right?

  7. # lijoon 27 Jan 2010 at 8:11 pm

    62.5?

  8. # Bill the Lizardon 27 Jan 2010 at 10:12 pm

    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.

  9. # TheMachineCharmeron 28 Jan 2010 at 10:33 am

    22(obese)=16(male) + 6(female)

    16(male)/22(obese) = whatever .

    is the answer I think.

  10. # Debajyoti Dason 28 Jan 2010 at 11:01 am

    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 :)

  11. # piyush goelon 28 Jan 2010 at 2:09 pm

    Its a standard application of Bayes Theorem.

    P(man|obese) = (0.4*0.4)/(0.4*0.4 + 0.6*.1)
    = 0.727

  12. # Nisha Palanion 18 Feb 2010 at 12:19 pm

    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

  13. # Nisha Palanion 18 Feb 2010 at 12:20 pm

    sorry in the last line I meant 16/40=2/5

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