Question

Find the probability for the experiment of drawing two marbles (without replacement) from a bag containing four green, four yellow, and three red marbles.

The marbles are of different colors.

Answer 1

Answer: There are 11 marbles in the bag, so the total number of ways to draw two marbles without replacement is:

11C2 = (1110)/(21) = 55

Now, we need to find the number of ways to draw two marbles of different colors. There are three possibilities:

Green and yellow: There are 4 green marbles and 4 yellow marbles to choose from. The number of ways to choose one green and one yellow marble is:

4C1 * 4C1 = 4*4 = 16

Green and red: There are 4 green marbles and 3 red marbles to choose from. The number of ways to choose one green and one red marble is:

4C1 * 3C1 = 4*3 = 12

Yellow and red: There are 4 yellow marbles and 3 red marbles to choose from. The number of ways to choose one yellow and one red marble is:

4C1 * 3C1 = 4*3 = 12

So, the total number of ways to draw two marbles of different colors is:

16 + 12 + 12 = 40

Therefore, the probability of drawing two marbles of different colors is:

40/55 = 8/11

Answer: 8/11

Explanation: