yes, good job
however, you should reduce 26/56 to 13/28
I figured out that the probability that both marbles are red is 20/56 and the probability that both are green is 6/56. Then I added them together to get 26/56. Is this correct? Thanks!
however, you should reduce 26/56 to 13/28
Let's start with the probability of drawing two red marbles.
First, we know that there are a total of 8 marbles in the jar (5 red marbles + 3 green marbles). When the first marble is drawn, there are now 7 marbles left in the jar, with 4 of them being red.
Therefore, the probability of drawing a red marble on the first draw is 5/8.
Now, since the marble is not replaced, there are now 6 marbles left in the jar, with 3 of them being red. The probability of drawing a red marble on the second draw, given that the first one was red, is 3/7.
To find the probability of both marbles being red, you multiply the probabilities of the two draws together: (5/8) * (3/7) = 15/56.
Similarly, you can calculate the probability of both marbles being green.
The probability of drawing a green marble on the first draw is 3/8.
With the marble not being replaced, there are now 7 marbles left in the jar, with 2 of them being green. The probability of drawing a green marble on the second draw, given that the first one was green, is 2/7.
To find the probability of both marbles being green, you multiply the probabilities of the two draws together: (3/8) * (2/7) = 6/56.
Finally, you add the probabilities of both marbles being red and both marbles being green together: 15/56 + 6/56 = 21/56.
So, the correct probability of both marbles being the same color is 21/56 which simplifies to 3/8.