A jar contains four marbles, each a different color: red, blue, green, and yellow. If you draw two marbles from the jar, one after another, replacing the first before drawing the second, what is the probability of getting

a. two red marbles?

b. a red marble on the first draw and a green marble on the second draw?

c. at least one red marble and one green marble?

d. no yellow marbles?

could someone please help me with this question

Sure! I can help you with that.

To find the probabilities, we need to calculate the number of successful outcomes (desired outcomes) and divide it by the total number of possible outcomes.

Now, let's solve each part of the question one by one:

a. Two red marbles:
In this case, the desired outcome is drawing two red marbles. Since there are four marbles in total, and each draw is replaced, the probability of getting a red marble on the first draw is 1 out of 4 (1/4), and the probability of getting a red marble on the second draw is also 1 out of 4 (1/4).

To find the probability of both events happening, we multiply the probabilities: (1/4) * (1/4) = 1/16. Therefore, the probability of getting two red marbles is 1/16.

b. A red marble on the first draw and a green marble on the second draw:
Here, we want to find the probability of getting a red marble on the first draw and a green marble on the second draw.

The probability of drawing a red marble on the first draw is 1 out of 4 (1/4), and since we replace the first marble, the probability of drawing a green marble on the second draw is also 1 out of 4 (1/4).

Again, we multiply the probabilities: (1/4) * (1/4) = 1/16. Therefore, the probability of drawing a red marble on the first draw and a green marble on the second draw is 1/16.

c. At least one red marble and one green marble:
To find this probability, we'll consider the complement rule.

The complement of "at least one red marble and one green marble" is "no red marble or no green marble." So, we'll find the probability of not getting either a red or a green marble and then subtract it from 1.

The probability of not getting a red marble on the first draw is 3 out of 4 (3/4), and the probability of not getting a green marble on the second draw is also 3 out of 4 (3/4).

Again, we multiply the probabilities: (3/4) * (3/4) = 9/16.

Finally, we subtract this probability from 1: 1 - 9/16 = 7/16. Therefore, the probability of getting at least one red marble and one green marble is 7/16.

d. No yellow marbles:
Since there are no yellow marbles in the jar, the probability of not getting a yellow marble on the first draw is 1, and the same goes for the second draw.

Therefore, the probability of not getting a yellow marble on either draw is 1 * 1 = 1.

Hence, the probability of not getting a yellow marble on both draws is also 1, which means the probability of no yellow marbles is 1.

I hope this explanation helps you understand how to calculate the probabilities in each case!