Question

We will remove two marbles from a jar that contains 3 green marbles, 2 blue marbles, 1 white marble, and 1 black marble. We might consider the conditional probability that the second marble we remove is green given that the first marble removed was green. Use the multiplication rule to calculate P( second green | first green). Convert your answer to a decimal and round to three decimal places.

Answer 1

P( second green | first green) = 1/3

Explanation:

There are 7 marbles in the jar in total

After the first pick, given the marble removes is green marbles, how many green marbles are there left in the jar? How many marbles are there left in the jar?

Green marbles left: 2

Marbles left: 6

Using the multiplication law of probability,

P(A∩B) = P(A) x P(B|A)

P(second green | first green) = P(second green and first green) / P(first green)

P(second green and first green) = 3/7 x 2/6 = 1/7

P(first green) = 3/7

∴(1/7) / (3/7) = 1/3

Thus, we come up to the conclusion P( second green | first green) = 1/3