Question

a bag contains 5 blue marbles 4 white marbles and 3 red marbles if 3 marbles are randomly selected from the bag what is the probability that exactly 2 of the 3 selected will be the same color

Answer 1

The probability that exactly 2 of the 3 selected marbles will be the same color is approximately 3.38%.

Step-by-step explanation:

To calculate the probability, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.

In this case, we want to find the probability of exactly 2 of the 3 selected marbles being the same color.

There are three possible scenarios:

1. Selecting 2 blue marbles and 1 marble of a different color (white or red)
2. Selecting 2 white marbles and 1 marble of a different color (blue or red)
3. Selecting 2 red marbles and 1 marble of a different color (blue or white)

Let's calculate the probabilities for each scenario.

Scenario 1:

The probability of selecting 2 blue marbles and 1 white marble is:

P(2 blue, 1 white) = (5/12) * (4/11) * (4/10) = 4/66 = 2/33

Scenario 2:

The probability of selecting 2 white marbles and 1 blue marble is:

P(2 white, 1 blue) = (4/12) * (3/11) * (5/10) = 3/55

Scenario 3:

The probability of selecting 2 red marbles and 1 blue marble is:

P(2 red, 1 blue) = (3/12) * (2/11) * (5/10) = 1/44

Now, we add up the probabilities of all three scenarios to get the overall probability:

P(exactly 2 of 3 marbles are the same color) = P(2 blue, 1 white) + P(2 white, 1 blue) + P(2 red, 1 blue) = 2/33 + 3/55 + 1/44 = 67/1980 ≈ 0.0338 or 3.38%.

Answer 2

2/12 or 1/6 because altogether there are 12 marbles and if you select 2 of the the chance is 2/12

correct me if i'm wrong