Two boxes contain chips of different colors. Whereas the first box has 45 red chips and 55 blue chips, the second box contains 70 red chips and 30 blue chips. You pick one chip from either of the boxes and it turns out to be blue. Given the facts above, what is the probability that the blue chip you picked came from the second box assuming that both boxes have the same probability of being chosen
Could someone help me with this question. I’m terrible at probability, just having a hard time in general understanding the concepts.
Also if anyone knows a good source for learning probability concepts please do suggest.
In this problem the number of the red chips is actually irrelevant. Think of it only in terms of the blue chips. There are 55 (box 1)+30 (box 2) = 85 total blue chips. What’s the chance that a random blue chip came from box 2? 30/85.
^ This way is very elegant and simple. Applying the classical Bayesian formula will also get you to the same answer, but give you more stress and writers’ cramp.
The loooong way:
Pr(box 2/blue) = Pr(box 2 and blue)/Pr(blue)
= Pr(blue/box 2) * Pr (box 2)/ [Pr(box 1 and blue) + Pr (box 2 and blue)]