Question

You have two boxes filled with colored marbles. The first box has 3 red marbles and 5 green. The second box has 2 red marbles and 4 green. You shuffle the marbles really well and without looking pull a marble out of the first box and place it into the second box. Then, again, without looking, you draw a marble from the second box. What is the probability of drawing a red marble from the second box?

Answer 1

The probability of drawing a red marble from the second box is 4/9.

Step-by-step explanation:

To find the probability of drawing a red marble from the second box, we need to consider the probability of two events happening:

1. Drawing a marble from the first box and placing it into the second box

2. Drawing a red marble from the second box

Let's break it down step by step:

1. Probability of drawing a marble from the first box = Total number of marbles in the first box / Total number of marbles (3 red + 5 green)
2. Probability of drawing a red marble from the second box = Number of red marbles in the second box / Total number of marbles in the second box

Since we are not replacing the marbles after drawing them, the probabilities are affected. Let's calculate:

1. Probability of drawing a marble from the first box = 8 / 8 = 1
2. Number of red marbles in the second box = 3 (initially) + 1 (transferred from the first box) = 4
3. Total number of marbles in the second box = 8 (initially) + 1 (transferred from the first box) = 9
4. Probability of drawing a red marble from the second box = 4 / 9

Therefore, the probability of drawing a red marble from the second box is 4/9.