Answer to Question #257107 in Statistics and Probability for Nevaeh

Question

A bag contains a $100 bill and two $20 bills. A second bag contains 1 gold marble and 2 silver marbles. You get to pick one bill out of the first bag. After this, you get to pick a marble out of the second bag. If you get the gold marble, you get to triple the amount of money you pulled from the first bag. If you get a silver marble, you get to double the amount of money you picked from the first bag. Build a probability model for all different amounts of money that you might win.

Answer 1

probability of taking $100 from first bag:

$P(\$100)=1/3$

probability of taking $20 from first bag:

$P(\$20)=2/3$

probability of taking gold marble from second bag:

$P(gold)=1/3$

probability of taking silver marble from second bag:

$P(silver)=2/3$

probability of getting $40:

$P(\$40)=P(\$20)\cdot P(silver)=2/3\cdot 2/3=4/9$

probability of getting $60:

$P(\$60)=P(\$20)\cdot P(gold)=2/3\cdot 1/3=2/9$

probability of getting $200:

$P(\$200)=P(\$100)\cdot P(silver)=1/3\cdot 2/3=2/9$

probability of getting $300:

$P(\$300)=P(\$100)\cdot P(gold)=1/3\cdot 1/3=1/9$