A jar contains 5 red marbles and 3 green marbles. A marble is drawn at random and not replaced. A second marble is then drawn from the jar. Find the probability that both marbles are the same color.
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!
You should reduce 26/56 to 13/28 yeah lol I agree
To find the probability that both marbles are the same color, you need to calculate the probability of drawing two red marbles and the probability of drawing two green marbles separately, and then add them together.
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.
yes, good job
however, you should reduce 26/56 to 13/28