What is probability of getting blue first and green second

Question

There are 10 marbles in bag 4 green 2 red and 4 blue. Amy chooses one marble then another without putting any back. What is probability that first one is blue and second one green.

Answer 1

Very easy, Amy! This sampling without replacement requires us to use conditional probability. The first marble doesn't depend on anything but the number of marbles:

P(blue) = 4 / 10

We have changed the bag now; it has one less marble, and one less blue. That means the probability of green is:

P(green|blue) = 4 / 9            ...because the  blue changed green.

We aren't done, though. These events followed one after another, so we multiply them:

(4 / 10) * (4 / 9) = 16 / 90  = 8 /45