There are 9 marbles if 3 different colors where 2 marbles are selected at random without replacement and the probability is 1/6
Is there a question buried in there somewhere?
I have no idea.
To solve this problem, we need to use the concept of probability. The probability of an event happening is the number of favorable outcomes divided by the number of total outcomes.
Let's break down the problem step by step:
Step 1: Determine the number of total outcomes.
We know that there are 9 marbles in total, and we are selecting 2 marbles without replacement. So, the total number of outcomes can be calculated using the combination formula: nCr = n! / (r!(n-r)!)
In this case, n = 9 (total number of marbles) and r = 2 (number of marbles selected). Plugging the values into the formula, we get:
9C2 = 9! / (2! * (9-2)!) = 9! / (2! * 7!) = (9 * 8) / (2 * 1) = 36
Therefore, the total number of outcomes is 36.
Step 2: Determine the number of favorable outcomes.
We know that the probability of selecting 2 marbles of different colors is 1/6. This means there is exactly one favorable outcome.
Step 3: Calculate the probability.
Now, we can calculate the probability using the formula: Probability = Favorable outcomes / Total outcomes.
In this case, we have 1 favorable outcome and 36 total outcomes:
Probability = 1 / 36
Therefore, the probability of selecting 2 marbles of different colors is 1/36, not 1/6 as mentioned in the question.
Please note that the question may have been either misunderstood or there might be an error in the given information. Nevertheless, the steps above explain how to solve a probability problem like this.