Question

A bag contains marbles of which 8 are blue; 5 are red; 3 are yellow, and 4 are orange. What is the probability of randomly drawing an orange marble, replacing it, and then drawing a blue marble?

Answer 1

The probability of drawing an orange marble, replacing it, and then drawing a blue marble from the bag is 2/25.

Step-by-step explanation:

To calculate the probability of drawing an orange marble, replacing it, and then drawing a blue marble, we need to treat each event independently since the marble is replaced after the first draw. There are 8 blue marbles, 5 red marbles, 3 yellow marbles, and 4 orange marbles, making a total of 20 marbles.

The probability of drawing an orange marble is the number of orange marbles divided by the total number, which is 4/20 or 1/5. After replacing the orange marble, the probability of then drawing a blue marble is 8/20 or 2/5. To find the total probability of both events occurring, we multiply the probabilities of each individual event:

Probability(Orange then Blue) = Probability(Orange) × Probability(Blue) = (1/5) × (2/5) = 2/25

The final probability of drawing an orange marble and then a blue marble, with replacement, is 2/25.