Binomial Probability Problems: Finding Probability for Glasses and DMF Teeth

[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 I am setting up these right or not.

 

[Stephen Tashi]

b. at least one wears them

compute 1.0 minus the probability that zero wear them.

c. at most one wears them

Add the probability that zero wear them and the probability that exactly 1 wears them.

 

[Bacle]

eMac:

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

 

[eMac]

eMac:

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

Because it said 50% of people over the age of 3. So 50% don't have it and then 50% of the 50% left don't have it, thus .25. At least I think.

 

[eMac]

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.

Thank you, this helped.

 

[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.

 

[eMac]

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.

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