Final answer:
To find the probability that the sample contains more red than yellow apples, calculate the probability of drawing 1 red apple and 0 yellow apples, and the probability of drawing 2 red apples and 0 yellow apples. Add the probabilities together.
Step-by-step explanation:
To find the probability that the sample contains more red than yellow apples, we need to consider all the possible outcomes where there are more red apples than yellow apples. There are two such possibilities: drawing 1 red apple and 0 yellow apples, or drawing 2 red apples and 0 yellow apples.
First, let's calculate the probability of drawing 1 red apple and 0 yellow apples. There are 5 red apples and 8 total apples, so the probability is 5/8.
Next, let's calculate the probability of drawing 2 red apples and 0 yellow apples. The probability of drawing the first red apple is 5/8, and since we're drawing without replacement, the probability of drawing the second red apple is 4/7. Therefore, the probability is (5/8)*(4/7) = 20/56.
Adding the probabilities from the two cases, the total probability is 5/8 + 20/56 = 25/28.