Math question help!

Question

A jar contains 4 red marbles and 5 yellow marbles. If 2 marbles are drawn (without replacement), what is the probability that they are both the same color?

Answer 1

Hi Jane,

You are starting with 4 red and 5 yellow marbles. You will need to figure the probability separately for each color, since they are different amounts.

Drawing two reds:

4:9 chance you draw a red (leaving 3 red and 5 yellow)

3:8 chance you draw another red (leaving 2 red and 5 yellow)

to find the odds of 2 red you multiply 4/9 by 3/8

Drawing two yellows:

5:9 chance your a yellow (leaving 4 red and 4 yellow)

4:8 chance you draw another yellow (leaving 4 red and 3 yellow)

to find the odds of 2 yellow you multiply 5/9 by 4/8

Answer 2

Event A is getting two red

Event B is getting two yellow

P(A) = (4/9)(3/8)

P(A) = 1/6

P(B) = (5/9))(4/8)

P(B) = (5/18)

P(A) or P(B) = 1/6 + 5/18

P(A) or P(B) = 4/9