Question

There are two folders, B₁ and B₂, from which the labels have been removed. However, it is known that B₁ contains the results of 2 pressure build-up tests and 3 injectivity tests; and that B₂ contains the result of 1 pressure build-up test and 4 injectivity tests. A sample of 2 tests is drawn from one of the folders and it turns out that one is pressure build-up result and one is injectivity test result. What is the probability that the folder from which the sample was drawn is B₁?

Answer 1

The probability of getting a pressure build-up test from B1 is, P(pressue|B1) = 2/5.
The probability of getting an injectivity test from B1 is P(injectivity|B1) = 3/5.
The probability that they came from B1 is, P(B1) = 1/2*2/5*3/5

Similarly,
The probability of getting a pressure build-up test from B2 is P(pressue|B2) =1/5.
The probability of getting an injectivity test from B1 is P(injectivity|B2) = 4/5.
​​​​​​​The probability that they came from B2 is, P(B2) = 1/2*1/5*4/5

Now, the probability that it came from B1 given we get a pressure build-up and an injectivity test is P(B1|pressure&injectivity) = P(B1) / P(B1) + P(B2) = (1/2*2/5*3/5) / (1/2*2/5*3/5) + (1/2*1/5*4/5)

= 6/50 / (6+4)/50
= 6/10
​​​​​​​= 3/5