Hello, db5vry!

As we say in The Corps, ya done good!

The events and are such that

Find:

is the complement of

So: .

2] The events and are such that:

Determine the value of in each of the cases when:

(a) and are mutually exclusive. .0.2 . . . . Right!

(b) and are independent.

(c)

(b) If and are independent: .

Substitute into: .

. . . . . . . . . . . . . . .

. . . . . . . . . . . . . .

(c)

From Bayes' Theorem: .

So we have: .

Substitute into: .

. . . . . . . . . . . . . . .

. . . . . . . . . . . . . .