Question

Alice has a bag of marbles consisting of 9 green marbles, 7 red marbles, 3 white marbles, and 6 yellow marbles. If she picks 2 of the marbles one after the other without replacing the first marble, what is the probability that the following will occur? Reduce all fractions!
A) The first marble was the color yellow and the second marble was the color white:


B) Both marbles were red in color:


C) What is the probability that Alice picks a red marble, puts it back in the bag, and then picks a green marble?

Answer 1

1. When solving similar problems, a tree diagram is a very useful method. Check the picture below for the solution of A:

the first pick can be either of the colors g, r, w or y, with a chance of 9/25, 7/25, 3/25 and 6/25 respectively.

After the first marble is yellow, now the second can be either of g, r, w, or y with chances 9/24, 7/24, 3/24, and 5/24 respectively.

Notice that the total number for the second choice is 25-1=24, since one is gone. In our case, one yellow, (this is why we now have 5/24)

So the P( that 1st is yellow, second is white) = (6/25)*(3/24)=3/100

B. P(both red)= (7/25)*(7/24)=49/600

C. P(1st red)=7/25
     P(green, after replacement)=9/25
     P(1.red,2.green)=(7/25)*(9/25)=63/625