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?

red maedle on the first draw.

1/2

To calculate the probability of these events, we need to consider the total number of possible outcomes and the number of favorable outcomes.

a. Probability of getting two red marbles:
Since there are four marbles in the jar and you're drawing with replacement, the total number of possible outcomes for each draw is still four. To calculate the probability of getting two red marbles, we need to determine the number of favorable outcomes, in this case, two red marbles.

Number of favorable outcomes: 1 (red on the first draw) x 1 (red on the second draw) = 1

Probability = Number of favorable outcomes / Total number of possible outcomes
= 1 / 4 x 4 (since there are two draws)
= 1/16

Therefore, the probability of getting two red marbles is 1/16.

b. Probability of getting a red marble on the first draw and a green marble on the second draw:
Similar to the previous question, the total number of possible outcomes for each draw is still four. To calculate the probability of this specific sequence, we need to determine the number of favorable outcomes, which is one red marble on the first draw and one green marble on the second draw.

Number of favorable outcomes: 1 (red on the first draw) x 1 (green on the second draw) = 1

Probability = Number of favorable outcomes / Total number of possible outcomes
= 1 / 4 x 4 (since there are two draws)
= 1/16

Therefore, the probability of getting a red marble on the first draw and a green marble on the second draw is also 1/16.

c. Probability of getting at least one red marble and one green marble:
Here, we need to calculate the probability of drawing at least one red marble and at least one green marble. To do this, we'll subtract the probability of not getting any red marbles or any green marbles from the total probability.

Probability of not getting any red marbles: 3/4 (there are 3 non-red marbles) x 3/4 (there are 3 non-red marbles after one has been drawn and replaced) = 9/16

Probability of not getting any green marbles: 3/4 (there are 3 non-green marbles) x 3/4 (there are 3 non-green marbles after one has been drawn and replaced) = 9/16

Probability of not getting any red or green marbles: 9/16 (probability of not getting any red marbles) x 9/16 (probability of not getting any green marbles) = 81/256

Probability of getting at least one red and one green marble = 1 - Probability of not getting any red or green marbles
= 1 - 81/256
= 175/256

Therefore, the probability of getting at least one red marble and one green marble is 175/256.

d. Probability of getting no yellow marbles:
Since there are no yellow marbles in the jar, the probability of not drawing a yellow marble is 1. Thus, the probability of getting no yellow marbles is 1.