Binomial Probability Problems: Finding Probability for Glasses and DMF Teeth

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    Binomial Probability
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Discussion Overview

The discussion revolves around solving binomial probability problems related to the likelihood of individuals wearing glasses or contact lenses and the condition of children's teeth (DMF). Participants explore the setup of the problems, specifically focusing on the appropriate values for probability and the calculations needed for various scenarios.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant sets up the first problem with n=5 and p=0.25, but expresses confusion about the correct value for p and the variable y for different scenarios.
  • Another participant suggests calculating the probability of at least one person wearing glasses by subtracting the probability that none wear them.
  • For the scenario of at most one person wearing glasses, it is proposed to add the probabilities of zero and exactly one person wearing them.
  • There is a challenge regarding the choice of p=0.25, with one participant questioning this choice based on the information that 50% of people wear glasses.
  • A participant explains their reasoning for using p=0.25, suggesting it is based on a misunderstanding of the population distribution.
  • Another participant encourages re-evaluating the reasoning behind the probability choice, indicating that the assumption about the age distribution may not be accurate.
  • A later reply indicates a change to p=0.5 after reconsideration, acknowledging a potential overcomplication of the problem.

Areas of Agreement / Disagreement

Participants express differing views on the appropriate probability values to use in the problems, leading to a lack of consensus on the correct setup for the binomial probability calculations.

Contextual Notes

The discussion highlights potential ambiguities in the problem statements and assumptions about the population demographics, which may affect the probability calculations.

eMac
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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.
 
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eMac said:
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.
 
eMac:

Why are you using p=0.25, if 50% wear glasses?
 
Bacle said:
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.
 
Stephen Tashi said:
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.
 
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.
 
Stephen Tashi said:
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.
 

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