Probability with given probability problem

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Homework Help Overview

The problem involves calculating the conditional probability of passing examination A given that an interviewee is employed by a company. The context includes the probabilities of passing each exam and the ratio of candidates taking each exam.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the overall probability of employment and how it relates to passing examination A. There are suggestions to visualize the problem using a large sample size and to consider tabular or tree diagram methods for organizing the probabilities. Some participants question the best approach to take without using Bayes' theorem.

Discussion Status

Participants are exploring different methods to approach the problem, including tabular representations and tree diagrams. There is a focus on understanding conditional probabilities and how to calculate them based on the given ratios and probabilities of passing. Some guidance has been offered regarding potential methods, but no consensus has been reached.

Contextual Notes

Participants express uncertainty about the implications of the "given" condition in the problem. There is also a mention of a large number of candidates to facilitate calculations, which may not be explicitly stated in the problem but is suggested as a useful approach.

kenny1999
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Homework Statement



In order to be employed by a particular company, the interviewee has to attend one of two examination A and B and pass the exam. According to past experience, probability of passing examination A is 2/5 and that of B is 1/4. The ratio of interviewee attending examination A and B is 3:2

Given that the interviewee is employed by the company, what is the probability of he passing examination A?

Homework Equations


The Attempt at a Solution

No ideas at all. I always fear "given"
 
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Hi kenny!

Start with, what is the probability that he will be employed by the company? :wink: Call this probability P(I)

Then think, with what probability in that total, are his chances of passing A?

Mathematically speaking, you are trying to find out what P(A|I) is.
 
kenny1999 said:

Homework Statement



In order to be employed by a particular company, the interviewee has to attend one of two examination A and B and pass the exam. According to past experience, probability of passing examination A is 2/5 and that of B is 1/4. The ratio of interviewee attending examination A and B is 3:2

Given that the interviewee is employed by the company, what is the probability of he passing examination A?

Homework Equations





The Attempt at a Solution




No ideas at all. I always fear "given"

Sometimes the best way to deal with this type of problem is to imagine a large number of candidates, say 5,000. How many of these write exam A? How many write exam B? Of those who write A, how many pass? Ditto for those who write B? Put all these numbers into a table.

So, the probability of passing is the number who pass A plus the number who pass B, all divided by 5000. You want a _conditional_ probability P(wrote A|pass). Can you see how to get that in terms of all the tabular entries?

Another way some people prefer is to draw a "tree diagram". In the first fork of the tree we have two branches "write A" and "write B". At the end of each of these two branches we have forks with additional branches "pass" or "fail". You can attach probabilities to each branch, then multiply them to get the probability at each of the four "tips".

A third way (which just formalizes the other two) is to use Bayes formulas; these are found in any textbook on the subject.

RGV
 
Ray Vickson said:
Sometimes the best way to deal with this type of problem is to imagine a large number of candidates, say 5,000. How many of these write exam A? How many write exam B? Of those who write A, how many pass? Ditto for those who write B? Put all these numbers into a table.

So, the probability of passing is the number who pass A plus the number who pass B, all divided by 5000. You want a _conditional_ probability P(wrote A|pass). Can you see how to get that in terms of all the tabular entries?

Another way some people prefer is to draw a "tree diagram". In the first fork of the tree we have two branches "write A" and "write B". At the end of each of these two branches we have forks with additional branches "pass" or "fail". You can attach probabilities to each branch, then multiply them to get the probability at each of the four "tips".

A third way (which just formalizes the other two) is to use Bayes formulas; these are found in any textbook on the subject.

RGV
sorry for late reply, i was not able to use cmoputer for a few days. two further questions about this. Thanks for replies.

1. In your first method.

Do you mean that I first caluclate the probability of P(Pass), then the resulting solution is = P(A | Pass) = P( A and Pass) / P ( Pass) ??

Anymore thing to take care of? Thank you

2. without using the concept of Bayes formula, is it the second method the best way to start with such kind of problems?
 
Last edited:
Yes, the best way to do problems like this is exactly what Ray Vinson said! Have you tried at all? Suppose there are 5000 applicants. Since the ratio of "A to B" is 3: 2, 3/5, or 3000, take exam A, 2/5, or 2000 take exam B. Since 2/5 pass exam A, 2/5 of 3000, or 1200, pass exam A. Since 1/4 pass exam B, 1/4 of 2000, or 500 pass exam B.

So how many people passed one of the exams (and so were hired)? Of those how many passed exam A?
 

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