Hello, amul28!
An interesting problem . . . It takes a bit of Thinking.
What does minimum and maximum values of a conditional probability mean?
When
Bayes' Theorem: .
And we have: . .[1]
What is the range of values for ?
The Venn diagram looks like this:
Code:
* - - - - - - - - - *
| |
| *-------* |
| | A | |
| |0.2*---+---* |
| | | | | |
| | |0.1| | |
| *---+---* | |
| | B | |
| *-------* |
| |
* - - - - - - - - - *
We are told that: .
That goes in the region common to circles and
We are told that: .
The 0.3 goes in the entire -circle.
That leaves 0.2 for the region,
. . the region that is in , but not in
What values can go in the region ?
. . The value can range from to .
Hence, can range from 0.1 to 0.8.
Substitute into [1].