A bag contain 2 white and 2 black ball. Another bag contain 2 white and 4 black ball. A bag and a ball are picked at random. What is the probability that the ball drawn is white

Answer 1

A tree diagram is useful in this type of problem:

The probability the ball will be white is 2/8 + 2/12 = 5/12

Answer 2

Hi Huidrom S.,

What you must do here is consider the order in which choices are made. In particular here, you must pick a bag at random, before you pick a ball at random. So figure the P(white) for each of the bags, then arithmetically average those probabilities. If you erroneously combined all the balls, then picked at random, you would obtain a different probability; you would only get the same probability if each of the bags contained the same number of balls. You can intuitively understand this, as you are averaging several fractions (probabilities), and you know that you must then cross-multiply by the denominators (unless they are equal!) on the way to calculating a final result!

-- Cheers, -- Mr. d.