Carson has a bag of 15 marbles. The bag has 8 red marbles, 4 blue marbles, and 3 green marbles. Carson randomly picks a
marble, replaces it in the bag, and randomly picks another
marble. Find the probability of each event.
(12) picking two blue marbles
(13) picking a red marble and then picking a blue marble
(14) picking a green marble and then a blue marble
(15) picking two red marbles

Start with the probability of any single situation.

Picking a red marble: 8/15
Picking a blue marble: 4/15
Picking a green marble: 3/15

Now, because the first marble pulled is put back, each draw is independent of what just happened. (In other words, the first marble pulled doesn’t impact the next drawing.)

Because the drawings are independent, you can just multiply the individual probabilities for each question.

Two blue marbles: 4/15 * 4/15 = 16/225
Red and then blue: 8/15 * 4/15 = 32/225
And so on…

That’d be 9 years or something