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Binomial Probability

  1. Sep 15, 2011 #1
    Problem 1: About 50% of all persons age 3 and older wear glasses or contact lenses. For a randomly selected group of five people find the probability that:
    a. exactly three wear glasses or contact lenses
    b. at least one wears them
    c. at most one wears them

    For this problem I set n=5, p=.25, and q(1-p)=.75

    For (a) I used y=3, I set up a combination of (5 choose 3) * ((.25)^3) * ((.75)^2)

    For (b) and (c) I'm confused as to what I should choose for (y).

    Problem 2: If 25% of 11-year old children have no decayed, missing, or filled (DMF) teeth, find the probability that in a sample of 20 children there will be:

    a. exactly 3 with no DMF teeth
    b. 3 or more with no DMF teeth
    c. fewer than 3 with no DMF teeth
    d. exactly 5 with no DMF teeth

    I set n=20, p=.25, and q(1-p)=.75

    I'm not sure if Im setting up these right or not.
  2. jcsd
  3. Sep 15, 2011 #2

    Stephen Tashi

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    compute 1.0 minus the probability that zero wear them.
    Add the probability that zero wear them and the probability that exactly 1 wears them.
  4. Sep 15, 2011 #3

    Why are you using p=0.25, if 50% wear glasses?
  5. Sep 15, 2011 #4
    Because it said 50% of people over the age of 3. So 50% dont have it and then 50% of the 50% left dont have it, thus .25. At least I think.
  6. Sep 16, 2011 #5
    Thank you, this helped.
  7. Sep 16, 2011 #6

    Stephen Tashi

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    Science Advisor

    I'm glad it helped. As Bacle pointed out, I think you should re-examine your reasoning about the using 0.25 in the first problem. Your thinking would only be correct if 50% of the population were less than 3 years old. The problem isn't phrased precisely, but it's probably best to assume none of the 5 people is less than 3 years old.
  8. Sep 16, 2011 #7
    Yea, I changed it to .5, I guess I was trying to look too deep into the problem.
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