1. Not finding help here? Sign up for a free 30min 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!

Probability problem

  1. Feb 29, 2004 #1
    Here's the question:
    A box contains 6 good and 8 defective light bulbs. The bulbs are drawn out one at a time, without replacement, and tested. What is the probability that the fifth good item is found on the ninth test?

    Could someone explain how I would go about solving this problem? Thanks!!
  2. jcsd
  3. Feb 29, 2004 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    If I told you the probability that exactly 4 good items have been found within 8 tests was 0.68, could you solve the problem?

    (p.s. 0.68 is probably wrong)
  4. Mar 6, 2004 #3
    Consider the first 9 balls, this can be done 14C9 ( from 14 choose 9 its on your calculator). If the 9th ball is the 5th good then the first 9 balls must consist of 5 good and 4 bad balls.
    The probability of this happening is 6C5*8C4/14C9. If this is true you need the 9th ball to be good. This has probably 5/9.
    So the probability is 6C5*8C4/14C9 * 5/9.
  5. Mar 6, 2004 #4

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    Not sure about that answer, Damned.

    You want 4 good and 4 bad on the first 8, then to draw a bad on the 9th, which is to draw on of the 4 remaining bad ones from the 6 that are left.


    but they might well be the same after simplifying
    Last edited: Mar 6, 2004
  6. Mar 6, 2004 #5
    The fifth good item has to found on the 9th test. So you should replace the 4/6 with a 2/6 and this can be rearranged to give my answer. You solution is slighty better and more consistent with student examples of negative binomial etc.
    Last edited: Mar 6, 2004
  7. Mar 6, 2004 #6

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    Sorry for switching things over, and yes I agree with your answer entirely now I've thought about it for a second. I also agree that such conditional probabilities would be beyond the scope of the course I imagine the OP is doing.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Probability problem
  1. Probability Problem (Replies: 3)

  2. Probability Problem (Replies: 1)

  3. Probability Problem (Replies: 1)

  4. Probability problem (Replies: 5)