Final answer:
The probability that both Robert and Matt are selected for the basketball team is calculated by multiplying the individual probabilities of each event, which are independent of each other. The combined probability is (1/7) × (2/9), corresponding to 2/63.
Step-by-step explanation:
To determine the probability that both Robert and Matt are selected for the basketball team, we need to assume that these events are independent. This means that the outcome of one event does not affect the outcome of the other. We use the rule that for independent events, the probability that both events A and B occur is the product of the probabilities of each event occurring separately.
The probability of Robert making the team is given to be 1/7, and the probability of Matt making the team is given to be 2/9. Therefore, to find the combined probability of both events happening, we multiply these two probabilities:
Probability(Robert and Matt both make the team) = Probability(Robert makes the team) × Probability(Matt makes the team)
Probability(Robert and Matt both make the team) = (1/7) × (2/9)
Probability(Robert and Matt both make the team) = 2/63
So, the correct answer is c) 2/63.