Question

A bag contains 3 blue marbles, 10 green marbles, 4 yellow marbles, and 8 red marbles. A marble is chosen at random, not replaced, then another marble is chosen. What is the probability that it is a red marble, then a blue marble? Write your answer as a fraction in simplest form.

Answer 1

The probability of drawing a red marble, and then a blue marble is 1/25.

Step-by-step explanation:

To calculate the probability of drawing a red marble, and then a blue marble, we need to consider that the first marble is not replaced after it is drawn. In this case, 8 total marbles are remaining in the bag after the first marble is drawn. The probability of drawing a red marble as the first marble is 8/25. After the red marble is drawn, there are now 24 marbles left in the bag, with 3 of them being blue. So, the probability of drawing a blue marble as the second marble is 3/24. To find the probability of both events occurring, we multiply the probabilities together: (8/25) * (3/24) = 1/25.

Answer 2

There are a total of 25 marbles in the bag.

The probability of choosing a red marble first is 8/25 since there are 8 red marbles out of 25 marbles in the bag.

Since a marble is not replaced after the first selection, there are now 24 marbles in the bag. There are still 3 blue marbles in the bag.

The probability of choosing a blue marble second, after a red marble has already been selected, is 3/24 or 1/8 since there are 3 blue marbles left out of 24 marbles in the bag.

To find the probability of both events occurring together, we multiply their individual probabilities:

8/25 x 1/8 = 1/25

Therefore, the probability that a red marble is chosen first, followed by a blue marble, is 1/25.