Question

A bag contains 3 black, 3 white, and 4 red marbles. If 3 marbles are selected at random without replacement, what is the probability of getting 2 black marbles and one white marble? Round your answer to 3 decimal digits.

Answer 1

1. total marbles=10 marbles
2. from ur sample table 2 Black marbles and one White is: pr(BWB or BBW or WBB)
3. which is:(18/720)+(18/720)+(18/720) = 54/720.
4. in the lowest term is 3/40

Answer 2

probability formula:

Probability = (Number of ways to get the desired outcome) / (Total number of ways to draw 3 marbles)

The number of ways to get 2 black marbles out of the 3 is given by the binomial coefficient "C(3, 2)", which is calculated as follows:

C(3, 2) = 3! / (2! * (3 - 2)!) = 3

The number of ways to get a cue ball out of the 3 is given by the binomial coefficient "C(3, 1)", which is calculated as follows:

C(3, 1) = 3! / (1! * (3 - 1)!) = 3

The total number of ways to draw 3 marbles among the 10 marbles (3 black + 3 white + 4 red) is given by the binomial coefficient "C(10, 3)", which is calculated as follows:

C(10, 3) = 10! / (3! * (10 - 3)!) = 120

probability calculation:

Probability = (Number of ways to get 2 black marbles and 1 white marble) / (Total number of ways to draw 3 marbles)

Probability = (3 * 3) / 120

Probability = 9 / 120

Probability ≈ 0.075

So the probability of getting 2 black marbles and 1 white marble by randomly drawing 3 marbles without replacement is approximately 0.075, rounded to 3 decimal digits.

Explanation: