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].