1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Find P(X = 3) porbability

  1. Jul 7, 2009 #1
    1. The problem statement, all variables and given/known data

    Suppose that 0.03% of plastic containers manufactured by a certain process have small
    holes that render them unfit for use. Let X represent the number of containers in a
    random sample of 10,000 that have this defect. Find P(X = 3).

    2. Relevant equations

    3. The attempt at a solution

    10000 choose 3

    i bet this actually does equal the answer maybe, but my calculator of course spits out 0 since .97^9997 is really really tiny...and doesnt take into account that 10000 choose 3 is humungo

    the answer is .224, but i cant match it
  2. jcsd
  3. Jul 7, 2009 #2


    User Avatar
    Science Advisor

    Re: probability

    It's not that hard to work it out "by hand".

    [tex]\left(\begin{array}{c}10000 \\ 3\end{array}\right)= \frac{10000!}{3!9997!}[/tex]
    [tex]= \frac{10000(9999)(9998)}{6}=\frac{10000}{2}\frac{9999}{3}(9998)[/tex]
    [tex]= 166616670000[/tex]

    Now, .033=0.000027 and (this is the hard one) .979997 is about .6 x 10-133. Since 166616670000 is about 1.7 x 1011 that product will be on the order of 1011- 5- 133= 10-127.

    However, is the proportion of of "unfit" cups .03% or 3%? You say ".03%" but you use 3%. If the correct value is .03%, then you want
    [tex]\left(\begin{array}{c}10000 \\ 3\end{array}\right)(.0003)^3)(.9997)^{9997}[/tex]
    Now that would be about .224.
    Last edited by a moderator: Jul 7, 2009
  4. Jul 8, 2009 #3
    Re: probability

    i was sitting in class today and wondered if i can use poisson distribution on this?

    o and yes that is my mistake that problem is copy and pasted, so yes it is actually 0.03% PERCENT...i didnt notice

    edit: ah yes i figured it out, [tex]\lambda[/tex] = .0003*10000 = 3


    [tex]\frac{e^{-3}*3^{3}}{3!}[/tex] = .224

    thanks alot though
    Last edited: Jul 8, 2009
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook