Suppose you have two bags of marbles that are in a box. Bag 1 contains 7 white marbles, 6 black marbles, and 3 gold marbles. Bag 2 contains 4 white marbles, 5 black marbles, and 15 gold marbles. The probability of grabbing the Bag 1 from the box is twice the probability of grabbing the Bag 2.

If you close your eyes, grab a bag from the box, and then grab a marble from that bag, what is the probability that it is gold?

Part a)

Solve this problem by hand. This should give us a theoretical value for pulling a gold marble.