Binomial Probability

1. Sep 15, 2011

eMac

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. Sep 15, 2011

Stephen Tashi

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.

3. Sep 15, 2011

Bacle

eMac:

Why are you using p=0.25, if 50% wear glasses?

4. Sep 15, 2011

eMac

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.

5. Sep 16, 2011

eMac

Thank you, this helped.

6. Sep 16, 2011

Stephen Tashi

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.

7. Sep 16, 2011

eMac

Yea, I changed it to .5, I guess I was trying to look too deep into the problem.