A bag of marbles contains 5 red, 3 blue, 2 green, and 2 yellow marbles.
What is the probability that you choose a red marble and then a green marble assuming you replace the first marble?
A)
1/
24
B)
5/
72
C)
5/
66
D)
5/
6
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
5/12 * 2/12 = ?
5/36
1/24
To find the probability of choosing a red marble and then a green marble, assuming you replace the first marble, you need to calculate the probability of choosing a red marble and then multiply it by the probability of choosing a green marble.
The total number of marbles in the bag is:
5 (red) + 3 (blue) + 2 (green) + 2 (yellow) = 12 marbles
The probability of choosing a red marble on the first draw is:
5 (red marbles) / 12 (total marbles) = 5/12
Since we are assuming that the first marble is replaced, the total number of marbles remains the same for the second draw. Therefore, the probability of choosing a green marble on the second draw is also:
2 (green marbles) / 12 (total marbles) = 1/6
To find the probability of both events happening, you multiply the probabilities:
(5/12) * (1/6) = 5/72
Therefore, the correct answer is B) 5/72.