Bayes' Theorem with Marbles

Update beliefs about bags based on draws

Identifying the Mystery Bag

You have three bags with different compositions. You pick one at random and draw a marble. Based on the color, which bag is most likely?

red: 5

blue: 5

Total: 10 marbles

Bag 1

5 red, 5 blue

red: 8

blue: 2

Total: 10 marbles

Bag 2

8 red, 2 blue

red: 2

blue: 8

Total: 10 marbles

Bag 3

2 red, 8 blue

Prior: Each bag is equally likely to be picked:

Bag 1:

Bag 2 (highest):

Bag 3:

Given you drew red, Bag 2 is most likely with a 53.3% probability.

Bag 1

33.3%

Bag 2

53.3%

Bag 3

13.3%

If you drew blue instead, the probabilities would flip:

Bag 1

33.3%

Bag 2

13.3%

Bag 3

53.3%