Hello, kakab00!

The events A and B are independent.

If it given that: .

(a) What is the value of ? By DeMorgan's Law: .

So we have: .

. . Hence: .

Events A and B are independent.

.. Hence: .

Formula: .

So we have: . .

Then: .

Therefore: .

(b) What is the value of ? We know that: .

. . Hence: .

By DeMorgan's Law: .

Therefore: .

(c) It is given that events B and C are mutually exclusive,

. . . and

What is the largest possible chance that event C will occur? Since and , then: .

. . (Circle is completely contained in circle .)

Since and are mutually exclusive, their circles do not intersect.

The Venn diagram looks like this: Code:

* - - - - - - - - - - - - - - - - - - - - - - - - - *
| |
| *---------* *---------* |
| / A \ / B \ |
| / × \ |
| / 0.05 / \ 0.60 \ |
| * * * * |
| | | | | |
| | *---* | | | |
| | / \ | 0.20 | | |
| | * * | | | |
| | | C | | | | |
| * * * * * * |
| \ \ / \ / / |
| \ *---* × / |
| \ / \ / |
| *---------* *---------* |
| 0.15 |
* - - - - - - - - - - - - - - - - - - - - - - - - - *

Since circle could be __equal__ to circle