Question

Can someone please explain "reverse conditions" when discussing conditional probability?

Answer 1

in probability we are sometimes given P( A | B) , and asked to determine P (B | A )

Answer 2

P ( A | B ) = prob. of A given B

P( B | A ) = prob. of B given A

Answer 3

So if you were given a simple question that asked you to find P(B|A) given P(A|B), could you just switch their roles to find the probability?

Answer 4

Could you maybe give an example of how a situation might be phrased that would require the use of reverse conditions?

Answer 5

you need more information

Answer 6

the classic example is with detection of a disease , using a test

Answer 7

i found this while googling
A disease is known to be present in 2% of a population. A test is developed to help
determine whether or not someone has the disease.
Given that a person has the disease, the test is positive with probability 0.95
Given that a person does not have the disease, the test is positive with probability 0.03

A person is selected at random from the population and tested for this disease.
Find the probability that the test is positive.

A doctor randomly selects a person from the population and tests him for the disease.
Given that the test is positive, find the probability that he does not have the disease.

Answer 8

first thing i usually do is label events. Let
S = event person has disease
F = event person does not have disease
+ = event person tests positive
- = event person does not test positive

Answer 9

this is a pretty good explanation here
http://www.algebra.com/algebra/homework/Probability-and-statistics/THEO-20091113.lesson