WOLFRAM|DEMONSTRATIONS PROJECT

Total Probability and Bayes's Theorem

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elements
2
3
4
5
reset
S
P(S)
P(X = A | S)
P(X = B | S)
pentagon(X)
1
6
0
1
triangle(X)
2
3
3
4
1
4
¬white(X)
1
4
0
1
¬pentagon(X)
5
6
3
5
2
5
gray(X)∨pentagon(X)
1
3
0
1
white(X)∧¬square(X)
2
3
3
4
1
4
¬white(X)∧pentagon(X)
1
3
0
1
¬gray(X)∧¬pentagon(X)
2
3
3
4
1
4
This Demonstration provides examples of total probability and Bayes's theorem. In the given world a figure X is randomly chosen. What is the probability of the given statement S? Suppose the statement is true. What is the probability that X = A? What is the probability that X = B?
If the probability of S is 0, the conditional probability P(X=A|S) is undefined (or undecided, denoted by U).
A simple two-dimensional area is occupied by white or gray triangles, squares, and pentagons. A disk means that the shape of the element is not known; in such a case a proposition of type Shape(
x
) has probability 1/3. A gray-white figure means that the color of the figure is not known; in such a case a proposition of type Color(x) has probability 1/2.