One bag contains 5 red marbles, 4 blue marbles, and 3 yellow marbles, and a second bag contains 4 red marbles, 6 blue marbles, and 5 yellow marbles. If Lydia randomly draws one marble from each bag, what is the probability that they are both not yellow?

The two draws are independent.

So the probability of getting a yellow in both bags is the product of the probability of getting a yellow in each bag.

P1(Y)=3/12
P2(Y)=5/15
So
P(Y,Y)=P1(Y)*P2(Y)

ryrrr7o

1/12

The question asks the opposite... not yellow.

so 9/12 * 10/15 = .75 * .666 = 50%

Andrew has it right.

To find the probability that Lydia draws a marble that is not yellow from both bags, we need to calculate the probabilities of drawing a non-yellow marble from each bag separately and then multiply them together.

In the first bag, there are a total of 5 red marbles, 4 blue marbles, and 3 yellow marbles. So the probability of drawing a non-yellow marble from the first bag is the total number of non-yellow marbles (red + blue) divided by the total number of marbles in the bag:

Probability of drawing a non-yellow marble from the first bag = (5 red marbles + 4 blue marbles) / (5 red marbles + 4 blue marbles + 3 yellow marbles)

Simplifying this, we get:

Probability of drawing a non-yellow marble from the first bag = 9 / 12

Next, let's calculate the probability of drawing a non-yellow marble from the second bag. In the second bag, there are 4 red marbles, 6 blue marbles, and 5 yellow marbles. So the probability of drawing a non-yellow marble from the second bag is:

Probability of drawing a non-yellow marble from the second bag = (4 red marbles + 6 blue marbles) / (4 red marbles + 6 blue marbles + 5 yellow marbles)

Simplifying this, we get:

Probability of drawing a non-yellow marble from the second bag = 10 / 15

Finally, to find the probability that both marbles drawn are not yellow, we multiply the probabilities of drawing a non-yellow marble from each bag together:

Probability that both marbles drawn are not yellow = Probability of drawing a non-yellow marble from the first bag * Probability of drawing a non-yellow marble from the second bag

Therefore,

Probability that both marbles drawn are not yellow = (9 / 12) * (10 / 15)

Now, we can simplify and calculate this probability:

Probability that both marbles drawn are not yellow = (3 / 4) * (2 / 3)

Simplifying this further, we get:

Probability that both marbles drawn are not yellow = 1 / 2

Therefore, the probability that Lydia draws marbles that are both not yellow is 1/2 or 0.5.