Problem Solving

rsarashi wrote:On a store counter are exactly two boxes containing only purple marbles and yellow marbles. Box A has 30 purple marbles and 20 yellow marbles; box B has 15 purple marbles and 35 yellow marbles. If Melanie randomly selects one of the boxes and then randomly selects one marble from that box, what is the probability that the marble selected will be purple?

A) 3/20
B) 3/10
C) 9/20
D) 3/5
E) 9/10

P(marble is purple) = P(Box A is selected AND a purple ball is selected from Box A OR Box B is selected AND a purple ball is selected from Box B)
= P(Box A is selected) x P(a purple ball is selected from Box A) + P(Box B is selected) x P(a purple ball is selected from Box B)
= 1/2 x 30/50 + 1/2 x 15/50
= 3/10 + 3/20
= 6/20 + 3/20
= 9/20

Answer: C

rsarashi wrote: ↑

Sat Sep 02, 2017 11:49 am

On a store counter are exactly two boxes containing only purple marbles and yellow marbles. Box A has 30 purple marbles and 20 yellow marbles; box B has 15 purple marbles and 35 yellow marbles. If Melanie randomly selects one of the boxes and then randomly selects one marble from that box, what is the probability that the marble selected will be purple?

A) 3/20

B) 3/10

C) 9/20

D) 3/5

E) 9/10

OAC

We are given that box A has 30 purple marbles and 20 yellow marbles and that box B has 15 purple marbles and 35 yellow marbles. We need to determine the probability, when selecting one marble from the box, of selecting a purple marble. Since we have two boxes, A and B, there are multiple scenarios to account for when selecting the marbles. We must account for the probability of first selecting either box and then secondly for selecting a purple marble. Let’s start with Box A.

P(selecting box A) = ½

P(selecting a purple marble in box A) = 30/50 = ⅗

Thus, the probability of selecting a purple marble from box A is ½ x ⅗ = 3/10

Next we can determine the probability of selecting a purple marble from box B.

P(selecting box B) = ½

P(selecting a purple marble in box B) = 15/50 = 3/10

Thus, the probability of selecting a purple marble from box B is ½ x 3/10 = 3/20

Now we can determine the probability of selecting a purple marble from box A or box B:

3/10 + 3/20 = 6/20 + 3/20 = 9/20.

Answer: C