A box contains 1 blue, 2 green, 1 red, and 2 yellow marbles. An experiment consists of randomly selecting two marbles without replacement. What is the probability of not obtaining a yellow marble?
To find the probability of not obtaining a yellow marble, we need to count the number of outcomes where we do not select a yellow marble and divide it by the total number of possible outcomes.
First, let's find the total number of possible outcomes. Since we are selecting two marbles without replacement, we can use combinations to calculate this. The total number of combinations of 7 marbles taken 2 at a time is given by the formula:
C(7, 2) = 7! / (2!(7 - 2)!) = (7 * 6) / (2 * 1) = 21
So, there are 21 possible outcomes.
Now, let's count the number of outcomes where we do not select a yellow marble. We have 1 blue, 2 green, 1 red, and 2 yellow marbles in the box. Since we want to exclude the yellow marbles, we have a total of 1 blue, 2 green, and 1 red marbles to choose from. We need to select 2 marbles from this reduced set.
Using the combination formula again, the number of combinations of 4 marbles taken 2 at a time is:
C(4, 2) = 4! / (2!(4 - 2)!) = (4 * 3) / (2 * 1) = 6
So, there are 6 outcomes where we do not select a yellow marble.
Therefore, the probability of not obtaining a yellow marble is:
6 / 21 = 2 / 7 ≈ 0.2857
So, the probability of not obtaining a yellow marble is approximately 0.2857 or 28.57%.