There are two unlabeled boxes, A and B. Each of the two boxes has 100 balls. Box A has 90 red balls and 10 white balls, and Box B has 20 red balls and 80 white balls. These two boxes have equal chance to be picked. Now a box is randomly picked and then a series of tests if performed on the box in order to make a good guess whether this box is A or B.
In each test, one ball is randomly picked from the box, its color is checked and then it's put back. Three tests were conducted, and 2 red balls were picked in the first two test and 1 white ball was picked in the third test.
Is the box more likely to be Box A or Box B ? How likely is the guess correct?
I tried to solve it this way:
A: it's box A B: it's box B R1: red on 1st test R2: red on 2nd test W3: white on 3rd test P(A) = P(R1|A) . P(R2|A) . P(W3|A) = 90/100 . 90/100 . 10/100 P(B) = P(R1|B) . P(R2|B) . P(W3|B) = 20/100 . 20/100. 80/100
I want to ask if my method is correct. Please advice.