Hello, ban26ana!

I wouldn't call this "conditional probability" . . .

This takes a lot of preliminary work . . . bear with me.There are three urns, A, B, and C.

Urn A contains 6 white balls and 4 black balls,

urn B contains 2 white balls and 6 black balls,

and urn C is empty.

Two balls are drawn at random from each of urn A and urn B,

and are placed into urn C.

Then a ball is drawn at random from urn C.

What is the probability the ball drawn from urn C is black?

Urn A

There are: . outcomes.

Urn B

There are: . outcomes.

Urn C

Now in each of these five cases, what is the probability of drawing a black ball?

Therefore: .

I need a nap . . .

.