The probability that the sample contains at least 2 yellow apples, we can consider two scenarios: Exactly 2 yellow apples and All 3 apples are yellow. By calculating the number of ways for each scenario and dividing by the total number of ways, the probability is approximately 0.6553.
The probability that the sample contains at least 2 yellow apples, we can consider two scenarios:
Exactly 2 yellow apples.
All 3 apples are yellow.
Let's calculate the probability for each scenario and then add them together.
Scenario 1: Exactly 2 yellow apples
The number of ways to choose 2 yellow apples out of 12 is given by the combination formula: C(12, 2).
The number of ways to choose 1 red apple out of 8 is given by the combination formula: C(8, 1).
So, the number of ways to choose exactly 2 yellow and 1 red apple is given by: C(12, 2) * C(8, 1).
Scenario 2: All 3 apples are yellow
The number of ways to choose 3 yellow apples out of 12 is given by the combination formula: C(12, 3).
So, the number of ways to choose all 3 yellow apples is: C(12, 3).
Now, the total number of ways to choose 3 apples out of 20 (8 red + 12 yellow) is given by: C(20, 3).
The probability is then calculated as the sum of the probabilities of these two scenarios divided by the total number of ways:
P(at least 2 yellow apples) = C(12, 2) * C(8, 1) + C(12, 3)} / {C(20, 3)}
Let's calculate this:
P(at least 2 yellow apples) = 66 * 8 + 220} / {1140}
P(at least 2 yellow apples) = 528 + 220} / {1140}
P(at least 2 yellow apples) = 748} / {1140}
P(at least 2 yellow apples) ≈ 0.6553
Therefore, the probability that the sample contains at least 2 yellow apples is approximately 0.6553 (rounded to four decimal places).