Final answer:
The probability that the sample contains all yellow apples is approximately 0.0242.
Step-by-step explanation:
To find the probability that the sample contains all yellow apples, we first need to determine the total number of possible samples that can be drawn. Since there are a total of 11 apples in the basket (7 red and 4 yellow), the number of possible samples is given by the combination formula: C(11, 3) = 165.
Next, we need to determine the number of samples that contain all yellow apples. Since there are 4 yellow apples in the basket, the number of such samples is given by the combination formula: C(4, 3) = 4.
Therefore, the probability that the sample contains all yellow apples is given by:
P(all yellow) = Number of favorable outcomes / Total number of outcomes = 4 / 165 ≈ 0.0242.