Probability :- Survival?

This SHOULD be fun!

one of those questions which tell you that maths IS beautiful :-)
this has two solutions, try to get both of them, you'll see what i mean!


Let 'm' the probability that a man aged 'x' years will die within a year. Let A1, A2, A3, A4......An be 'n' men aged 'x' years. Find the probability that out of these 'n' men, A1 not only dies within a year, but also is the first one to die.


-Sambhav

27 comments:

  1. AnonymousApril 29, 2011 at 3:52 PM

    submission (m^r)*((1-m)^n-r)*(n-1Cr-1) *(r-1!)

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  2. Sambhav GuptaApril 29, 2011 at 4:11 PM

    nope..

    btw, its 'summation'...means to 'sum'

    we are not submitting anything to anyone :P

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  3. shaanApril 29, 2011 at 4:12 PM

    This comment has been removed by a blog administrator.

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  4. Sambhav GuptaApril 29, 2011 at 4:19 PM

    that was quick shaan!
    well, i'll take care in future, im still an amateur blogger :P

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  5. guntashApril 29, 2011 at 4:32 PM

    This comment has been removed by the author.

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  6. shaanApril 29, 2011 at 4:33 PM

    nope guntash

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  7. guntashApril 29, 2011 at 4:34 PM

    This comment has been removed by the author.

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  8. ShivankerApril 29, 2011 at 4:41 PM

    suppose i say.. that A1 dies within a year.. is the probability m??

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  9. guntashApril 29, 2011 at 4:43 PM

    This comment has been removed by a blog administrator.

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  10. Sambhav GuptaApril 29, 2011 at 4:51 PM

    @shivanker, yes, and if you say that both A1 and A2 die within a year, the prob is m^2

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  11. ShivankerApril 29, 2011 at 4:56 PM

    then my answer is same as gunts..

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  12. shaanApril 29, 2011 at 5:15 PM

    shivanker
    if A1 dies in 1 yr-->
    u also gotto take into a/c others - ki woh zinda rahe yaa mare..:P

    so u multiply some more terms

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  13. Sambhav GuptaApril 29, 2011 at 5:19 PM

    no shaan, prob that A1 dies in a year is m only, but prob that 'only' A1 dies is what you are talking about

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  14. shaanApril 29, 2011 at 5:27 PM

    yes, i meant that only..

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  15. shaanApril 29, 2011 at 8:52 PM

    i'm not able to do it the PROBABILITY way,

    tried conditional prob, but din't go much far.:(

    pls tell a hint to that way too...

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  16. shaanApril 29, 2011 at 9:01 PM

    or do we have to draw tree diag , then arrive at the same thing as that binomial summation..?

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  17. Sambhav GuptaApril 29, 2011 at 9:23 PM

    will tell soon, im waiting for some more attempts

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  18. guntashApril 29, 2011 at 9:38 PM

    This comment has been removed by a blog administrator.

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  19. shaanApril 29, 2011 at 9:41 PM

    thanks guntash..

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  20. tushar guptaApril 29, 2011 at 10:43 PM

    m/n??? cud be wrong, my confidence(n accuracy) tends to dip b4 any exam :-(

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  21. shivamApril 30, 2011 at 9:07 AM

    is it [n-1cr-1(m¥r)(1-m)¥n-r]/r ¥ stands for ki power.

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  22. shivamApril 30, 2011 at 9:33 AM

    by base theorem getting 1/n. not sure at all

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  23. tushar guptaApril 30, 2011 at 11:40 AM

    i dont remember studying any "base thrm" :D

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  24. Tushar SinglaApril 30, 2011 at 12:22 PM

    I'm getting

    [ 1 -(1-m)^n ] /n


    http://latex.codecogs.com/gif.latex?\frac{1&space;-&space;(1-m)^{n}}{n}

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  25. Sambhav GuptaMay 1, 2011 at 12:53 AM

    yes, the correct answer is summation (n-1)C(r)[m^(r+1)][(1-m)^(n-r-1)]/(r+1) = [1-(1-m)^n]/n


    alternatively, the probability that at least one man dies within a year is [1-(1-m)^n], and the probability that A1 dies first is 1/n, multiply the two

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  26. Tushar SinglaMay 1, 2011 at 5:39 PM

    beauty..!

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