Hello, Punch!

The events are such that and are independent,

and and are mutually exclusive.

Given:.

Draw a Venn diagram.

and are mutually exclusive.Code:* * * * * * * * * * A * B * C * * * * * * * * * * * * * * * * * * * * 0.32 * 0.08 * * 0.1 * 0.2 * * * * * * * * * * * * * * * * 0.02 * * * * * * * * * * * * * * * *

. . Their circles do not intersect.

and are independent.

Hence:.

We can complete the Venn diagram.

(a) Calculate

Bayes' Theorem: .

From the Venn diagram, we see that:

. .

. .

(b) Calculate the probability that exactly one one of will occur.

From the Venn diagram, we see that:

. .

. .

Therefore:.