A bag contains 3 red marbles, 3 blue marbles and 3 yellow marbles. Which of the following methods of selecting 2 marbles will have the greater probability of choosing 2 red marbles?

Steve answered this above.

Don't know

7.2

To determine which of the given methods of selecting 2 marbles will have the greater probability of choosing 2 red marbles, let's analyze the options:

Option A: Choosing 2 marbles randomly from the bag without replacement.
Option B: Choosing 1 marble randomly from the bag, then choosing another marble randomly from the remaining marbles without replacement.

To find out the probability of selecting 2 red marbles for each option, we need to calculate the probability of selecting a red marble on each draw and multiply them together.

Option A:
In the first draw, the probability of selecting a red marble is 3/9 since there are 3 red marbles out of 9 total marbles.
After the first draw, there will be 2 red marbles left out of the remaining 8 marbles in the bag.
In the second draw, the probability of selecting another red marble is 2/8.

Therefore, the probability of selecting 2 red marbles using Option A is (3/9) * (2/8) = 1/12.

Option B:
In the first draw, the probability of selecting a red marble is 3/9, same as before.
After the first draw, there will be 3 red marbles left out of the remaining 8 marbles in the bag.
In the second draw, the probability of selecting another red marble is 3/8.

Therefore, the probability of selecting 2 red marbles using Option B is (3/9) * (3/8) = 1/8.

Comparing the results, we can see that the probability of choosing 2 red marbles is greater in Option B (1/8) than in Option A (1/12).

Hence, the method of selecting marbles that has the greater probability of choosing 2 red marbles is Option B: Choosing 1 marble randomly from the bag, then choosing another marble randomly from the remaining marbles without replacement.