Marble transferred, marble drawn
Setup:
- Bin 1 holds five red and four green marbles.
- Bin 2 holds four red and five green marbles.
Experiment:
- You take a random marble from Bin 1 and put it in Bin 2 and shake Bin 2.
- Then you draw a random marble from Bin 2 and look at it.
Questions:
(a) What is the probability you draw a red marble?
(b) Supposing that you drew a red marble, what is the probability that a red marble was transferred?
Solution
(1) Construct the tree diagram.
Identify sub-experiments, label events, compute probabilities:
(2) For (a), compute
Add up leaf numbers for
(3) For (b), compute
Conditional probability:
Plug in data and compute:
Interpretation: mass of desired pathway over mass of possible pathways.