Conditional Probability

Question

Box 1 contains 4 red chips and 1 white chip. Box 2 contains 3 red, 1 black and 6 white chips. The experiment consists of randomly picking a box, then randomly picking a chip from it. Find the probability that using demorgans law and probability trees.



1. A red chip is drawn from Box #1
2. A red chip is drawn, given that Box #1 was picked
3. Box #1 was picked, given that the chip is black

Answer 1

1. There is a 50% chance (1/2) of choosing box #1 and an 80% chance (4/5) of picking a red chip so P(red chip from box #1) = (1/2) * (4/5) = 4/10 = 40%
2. Since we are given that box #1 is picked, this takes away the 50% chance of choosing either box, therefore P(red chip given box #1) = 4/5 = 80%
3. Since we are given that box #1 is picked and there are no black chips in box #1, P(black chip given box #1) = 0%