Unequal chances and Bayes' law
Give each outcome its own weight and add them. Then read a tree backwards: a bad bolt is found, which machine made it?
- France: grade 12
- Germany: grade 11
- Iran: grade 11
- Russia: grade 10
Guide
This studio is for the Iranian Grade 11 statistics and probability book: unequal chances and Bayes' law.
Outcomes do not always have equal chances. If 1 is on three faces of a die, 2 on two faces and 3 on one, then 36, not one third. Write the probability of each outcome; the probability of an event is the sum of its outcomes' probabilities, and all of them add to 1.
In the tree the first branch says which machine made the bolt and the second says good or bad. If we know the bolt is bad we look only at the bad bolts: P(A given B) = P(A and B) ÷ P(B). Reading the tree this way round is Bayes' law.