Baye's Theorem

Connections List
 * Tools/Logic
 * Reasonable Faith

Scope
 * Baye's theorem

Topics
 * Use
 * Math
 * References

Use
 * States the probability of conditional probability (if A then B) given other information
 * Can be used to in cases of inductive reasoning.

MATH Math example Philosophy example
 * P(A|B)=P(B|A)*P(A)/P(B)
 * P(A|B)=  P(B|A)*P(A)   /   (P(B|A)*P(A) + P(B|notA)*P(notA))
 * E.g. test a random person for weed/drug. Test is 99% accurate for both A and B type errors. In population, 0.5% people use weed. Then, if a person tests positive, probability that they are guilty, P(guilty|pos), is
 * =P(pos|guilty)*P(guilty) /  (P(pos|guilty)*P(guilty) + P(pos|notGuilty)*P(notGuilty)
 * = true guilty / (true guilty + false guilty)
 * =0.99*0.005 / (0.99*0.005 + 0.01*0.995)
 * =0.33
 * A = H = premise/hypothesis, B = E evidence (specific). Also G = global background stuff. Probability you're right is:
 * P(H|E) = P(E|HandG)*P(H|G) / (P(E|HandG)*P(H|G) + P(E|notHandG)*P(notH|G))
 * prob that god exists given existence of universe = chance that god >> universe * probability of God / (god>>universe*prob of God + chance that no god >> universe * probability of not God)

REFERENCES
 * https://en.wikipedia.org/wiki/Bayes%27_theorem
 * William Lane Craig, Reasonable faith, pg 53