A jar contains 6 red marbles and 9 blue marbles. If Evelyn

swerve wrote:A jar contains 6 red marbles and 9 blue marbles. If Evelyn reaches into the jar and simultaneously draws two marbles at random, what is the probability that she will draw two marbles of the same color?

A. 2/7
B. 12/35
C. 3/7
D. 17/35
E. 25/35

P(both are same color) = P(1st marble is red AND 2nd marble is red OR 1st marble is blue AND 2nd marble is blue)
= [P(1st marble is red) x P(2nd marble is red)] + [P(1st marble is blue) x P(2nd marble is blue)]
= [6/15 x 5/14] + [9/15 x 8/14]
= [2/5 x 5/14] + [3/5 x 8/14]
= 10/70 + 24/70
= 34/70
= 17/35

Answer: D

Cheers,
Brent

There are two outcomes that meet the requirement either BB OR RR. When working with probability it boils down to putting want you want over the total number. When you have multiple fractions, typically AND means you need to multiply the fractions and OR means you need to add. So for this problem we can translate it into the following:

Red AND Red OR Blue AND Blue

Now plug values into this, keeping in mind on the second draw of each option you will have fewer marbles available, so this gives you

6/16*5/14 + 9/15*8/14

Cancel out common factors to make the numbers easier to work with.

1/1*1/7+3/5*4/7

Multiply and then add.

1/7 + 12/35 = 17/35.

So the answer is choice D.

Take care,
Sionainn