What is the product of these two probabilities

  • Context: Undergrad 
  • Thread starter Thread starter mcknia07
  • Start date Start date
  • Tags Tags
    Probabilities Product
Click For Summary

Discussion Overview

The discussion revolves around calculating probabilities related to cholesterol levels and drug usage. Participants explore the probabilities of cholesterol levels being less than or equal to 200, the probability of taking a drug, and whether these events are independent. The scope includes mathematical reasoning and conceptual clarification.

Discussion Character

  • Mathematical reasoning
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Participants define event A as "cholesterol ≤ 200" and event B as "took the drug".
  • One participant calculates the probability P(A) as 110/200, representing the percentage of people with cholesterol ≤ 200.
  • Another participant suggests calculating P(B) by determining the number of people who took the drug relative to the total population.
  • There is a discussion about the correct interpretation of the data, with some participants clarifying that 100 people took the drug.
  • One participant calculates the probability of taking the drug as 50% based on the provided data.
  • Participants discuss how to find the conditional probability P(A|B) and whether the events A and B are independent.
  • There is a disagreement regarding the definition of independence, with one participant asserting that the probabilities must add up to 1, while another clarifies that independence is determined by comparing P(A|B) and P(A).

Areas of Agreement / Disagreement

Participants generally agree on the calculations of P(A) and P(B), but there is disagreement regarding the definition of independence and whether the events are independent. The discussion remains unresolved on the criteria for independence.

Contextual Notes

Some calculations rely on interpretations of the data, and there are unresolved points regarding the definitions and conditions for independence in probability.

mcknia07
Messages
284
Reaction score
7
Took Drug Didn't Total
Cholesterol ≤ 200 60 50 110
Cholesterol > 200 40 50 90
100 100 200We’ll call event A “cholesterol ≤ 200” and event B “took the drug”…..

What is the probability a person’s cholesterol ≤ 200? P(A)
What is the probability a person took the drug? P(B)
What is the product of these two probabilities (multiply the above together)?
P(A) * P(B)
Given that a person took the cholesterol drug, what is the probability that their cholesterol ≤ 200? P(A|B)
Does P(A) * P(B) = P(A|B)?
Are these events independent?
What does this tell us about the effectiveness of the drug?

* * Help me please!
 
Last edited:
Physics news on Phys.org


Let's do the first one. What's the probability that somebody's cholesterol is ≤200

For this: what is the total population?? Which ones are ≤200 ?
 


Total of everyone is 200. 110 are equal to or greater than 200
 


mcknia07 said:
Total of everyone is 200. 110 are equal to or greater than 200

You probably meant to say smaller or equal than 200 :-p

Anyway. The P(A) is now easy: it's the percentage of people with cholesterol ≤200. So it's just 110/200.

Can you find P(B) is the same fashion?? That is:
- What's the number of people that took the drug
- What's the total population
- What's the percentage?
 


Yeah yeah, lol. You know what I meant :)
40/90
200
40/200

right??
 


mcknia07 said:
Yeah yeah, lol. You know what I meant :)
40/90
200
40/200

right??

Hmmm, not sure what you mean with those numbers...

How many people took the drug?? 40/90 doesn't make much sense, you will want an integer as an answer.

The bottom row gives us the information here. It tells us that 100 people took the drug, 100 people didn't and 200 people is the total population.

So what's the percentage of people that took the drug??
 


50% took it
 


mcknia07 said:
50% took it

OK, that's good!

So the answer to the first question is 110/200 and the second is 1/2.

So you can multiply these together and that gives the third question.

For the fourth, you're interested in all the people that actually took the drug. So the first column interests us here. So of all the people who took the drug, we have that

60 people have cholesterol ≤200
40 people have cholesterol >200
and 100 people in total took the drug.

Sooo, what's the percentage of people that took the drug with cholesterol ≤200??
 


3/10, I think, right?
 
  • #10


Did you do 60/200??

In this case, you calculated the people who tool the drug AND have cholesterol ≤200 and you divided it by the total population.

However, you are now interested ONLY in the people who took the drug. So the people who did not took the drug don't interest us and thus shouldn't be counted in the population.

So our population now is not 200 but 100.
 
  • #11


Ok, so it's 60/100??
 
  • #12


Good!

Now, we will want to know if the event are independent or not. Can you give me the definition of independence??
 
  • #13


The probability has to add up to 1. Yes, I did look it up :) So... I'm going to say it's not independent...
 
  • #14


mcknia07 said:
The probability has to add up to 1. Yes, I did look it up :) So... I'm going to say it's not independent...

Huh?? You're right that they are not independent. But your reason is not correct. That the probabilities add up to 1 has nothing to do with it here :frown:

Usually, we say that A is independent from B if P(A|B)=P(A). Translated in words, we have that the chance that A happens is the same as that chance that A happens given B. So it is irrelevant that B is true, because the chance that A happens remains the same anyway.

Now, is P(A|B)=P(A) here??
 
  • #15


I read it in my school book...
 
  • #16


mcknia07 said:
I read it in my school book...

I don't doubt it, but it's strange. Can you quote what's in your book??
 
  • #17


No, its not
 
  • #18


i can try to send a link... may just be directly linked to my account
 
  • #19
http://mycourses.mtc.edu/@@/95DC08FEE0579C04ED66E7A692617759/courses/1/BUS1150A.01.2.12/content/_514222_1/BUS1150-BH%20Text-Section%203.pdf

try that...
 

Similar threads

Undergrad Can I get thresholds from logistic regression coefficients?
  • · Replies 12 ·
Replies
12
Views
2K
Undergrad What is the probability that the product of the digits is odd?
  • · Replies 13 ·
Replies
13
Views
3K
What is the probability a person’s cholesterol
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Understanding extinction probability in simple GWP
  • · Replies 1 ·
Replies
1
Views
3K
MHB [ASK] Probability with Factors
  • · Replies 2 ·
Replies
2
Views
1K
High School How to calculate this conditional probability?
  • · Replies 7 ·
Replies
7
Views
1K
Undergrad Taking socks out of drawers, conditional probability
  • · Replies 36 ·
2
Replies
36
Views
5K
MHB Probability of O & AB Blood Types
  • · Replies 1 ·
Replies
1
Views
2K
MHB How to Show Equality of Probabilities?
  • · Replies 5 ·
Replies
5
Views
1K
Graduate Multiparticipant events and pairwise probabilities
  • · Replies 16 ·
Replies
16
Views
2K