The bag contains three red marbles, two blue marbles, and seven yellow marbles. Two marbles are randomly drawn from the bag. What is the probability of drawing a blue marble, replacing it, and then drawing a blue marble?

that would simply be 2/11 x 2/11 = 4/121

Rami draws a chip from the bag without looking. He keeps the chip and then draws antoher one from the bag. What is the probability that both chips are blue? 3 yellow, 2 brown, 5 green, 4 blue, an 2 red.

To find the probability of drawing a blue marble, replacing it, and then drawing another blue marble, we can multiply the probabilities of each event.

Let's break down the problem step by step:

Step 1: Probability of drawing a blue marble in the first draw
Since there are two blue marbles in the bag and a total of twelve marbles, the probability of drawing a blue marble in the first draw is 2/12.

Step 2: Probability of replacing the blue marble
Since we are replacing the first blue marble back into the bag, the total number of marbles remains the same. Therefore, the probability of drawing another blue marble is still 2/12.

Step 3: Multiply the probabilities
To find the probability of two independent events occurring, we can multiply the probabilities. So, the probability of drawing a blue marble, replacing it, and then drawing another blue marble is:
(2/12) * (2/12) = 4/144 = 1/36.

Therefore, the probability of drawing a blue marble, replacing it, and then drawing another blue marble is 1/36.