A box contains the following mixture of colored marbles: 2 black, 1 red, 4 yellow, and 2 green. If two marbles are drawn, the second being drawn after the first is replaced, then what is the probability that both are yellow?
I am stuck on this question for my math final
see your 3:13 post
To find the probability of drawing two yellow marbles from the box, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes: When drawing two marbles, each draw has four possibilities (black, red, yellow, or green). Since the first marble is replaced before drawing the second marble, each draw is independent. Hence, the total number of possible outcomes is 4 * 4 = 16 (4 possibilities for the first draw multiplied by 4 possibilities for the second draw).
Number of favorable outcomes: We want to draw two yellow marbles. There are four yellow marbles in the box, so for each draw, the probability of drawing a yellow marble is 4/16 = 1/4. Since the draws are independent, we can multiply the probabilities together. Hence, the number of favorable outcomes is (1/4) * (1/4) = 1/16.
Therefore, the probability of drawing two yellow marbles is 1/16.