A bag has 4 red marbles, 5 blue marbles, and 6 green marbles. What is the probability if choosing a red marble from the bag, putting it back, and then choosing a green marble?
4/15
6/15
10/15
24/225
the two events are independent because you put the first one back
4/15 * 6/15
To find the probability of choosing a red marble from the bag, putting it back, and then choosing a green marble, we need to find the probability of each event happening separately and then multiply them together.
Step 1: Calculate the probability of choosing a red marble.
In this scenario, there are 4 red marbles out of a total of 4 + 5 + 6 = 15 marbles in the bag. So, the probability of choosing a red marble is 4/15.
Step 2: Calculate the probability of choosing a green marble.
After putting the red marble back, the number of marbles in the bag remains the same. However, now there are 6 green marbles out of the total of 15 marbles in the bag. So, the probability of choosing a green marble is 6/15.
Step 3: Multiply the probabilities.
To find the probability of both events happening, multiply the probability of choosing a red marble (4/15) by the probability of choosing a green marble (6/15).
(4/15) * (6/15) = 24/225
Therefore, the probability of choosing a red marble from the bag, putting it back, and then choosing a green marble is 24/225.