Question

A bag contains 6 orange marbles and 7 green marbles. A marble is selected from the bag at random, set aside, and then another marble is selected. Which of the following choices shows the correct calculation of the probability that both marbles are orange?

Answer 1

To find the probability that both marbles are orange, we multiply the probability of selecting an orange marble on the first draw with the probability of selecting another orange marble on the second draw.

Step-by-step explanation:

To find the probability that both marbles are orange, we need to determine the probability of selecting an orange marble on the first draw and then selecting another orange marble on the second draw.

There are a total of 13 marbles in the bag (6 orange and 7 green), so the probability of selecting an orange marble on the first draw is 6/13.

After the first orange marble is selected, there are now 12 marbles left in the bag, including 5 orange marbles. Therefore, the probability of selecting another orange marble on the second draw is 5/12.

To find the probability of both events occurring, we multiply the individual probabilities together: (6/13) * (5/12) = 30/156 = 5/26.