Bayes Theorem
Paint events A and B onto a sample space grid and watch P(A), P(B), and P(A | B) update live.
ฮฉ
Draw a closed shape โ releasing connects the ends and fills
P(A)
P(B)
P(AโฉB)
P(A|B) B is empty
P(B|A) A is empty
Challenges
P(A|B) = 0 Draw A and B with no overlap
P(A|B) = 1 Draw B entirely inside A
ฮฉ โ 100 outcomes
P(A) 0 / 100 = 0.00
P(B) 0 / 100 = 0.00
P(AโฉB) 0 / 100 = 0.00
P(A|B) โ
P(AโฉB) / P(B)
P(B|A) โ
P(AโฉB) / P(A)
Challenges
P(A) = 0.25 Assign exactly 25 squares to A
P(A|B) = 0.5 Let exactly half of B's squares overlap with A
P(AโฉB) = 0.1 Put exactly 10 squares in both A and B
P(A|B) = P(B|A) Make A and B have the same number of squares