There are two boxes A and B. In box A, there are 3 red . . .

VJesus12 wrote:There are two boxes A and B. In box A, there are 3 red marbles and 5 green marbles. In box B, there are 2 red marbles and 3 green marbles. Jack rolls the dice. If the result is 1 or 6 then Jack will pick a marble from box A. If the result is neither 1 nor 6 then Jack will pick a marble from box B. What is the probability that the picked marble is green?

A. 1/8
B. 73/120
C. 21/40
D. 5/24
E. 25/56

We are given that in box A, there are 3 red marbles and 5 green marbles, and in box B, there are 2 red marbles and 3 green marbles. When the die is rolled, if the result is 1 or 6 then Jack will pick a marble from box A, and if the result if neither 1 nor 6 then Jack will pick a marble from box B. We need to determine the probability that a green marble is selected.

Notice that the probability that a green marble is selected is the probability that a green marble is selected from box A or from box B. That is, the probability of selecting a green marble is the probability that it’s selected from box A plus the probability that it’s selected from box B. Let’s start with box A.

P(rolling a 1 or 6) = 2/6 = 1/3

P(selecting a green marble) = 5/8

Thus, the probability of selecting a green marble from box A is 1/3 x 5/8 = 5/24.

Now we can move to box B.

P(not rolling a 1 or 6) = 2/3

P(selecting a green marble) = 3/5

Thus, the probability of selecting a green marble from box B is 2/3 x 3/5 = 2/5.

The probability of selecting a green marble from box A or box B is:

5/24 + 2/5 = 25/120 + 48/120 = 73/120

Answer: B