A box contains 7 red marbles and 3 blue marbles. Determine the probability of obtaining 2 red marbles if:

Question

An experiment consist of randomly selecting 2 marbles. Determine the probability of obtaining 2 red marbles if:

A. the first marble selected is returned to the box before the second marble is selected.

B. The first marble selected is not returned to the box for the selection of the second marble. 

Answer 1

First let’s name some variables to make the problem easier to solve:

R - red marble

B - blue marble

Next let’s look at what the box contains with just the letters:

RRRRRRR

BBB

A. This question is asking for the probability of drawing two red marbles with replacement:

P(2 red marbles) = (7/10)(7/10) = .490

B. This question is asking for the probability of drawing two red marbles without replacement:

P(2 red marbles) = (7/10)(6/9) = .467