Final answer:
The probability that Stephen Curry makes both free throws is found by multiplying the probability of making each free throw (.908) together, resulting in a probability of .824464, which closely matches Option 1: 0.827264, indicating a possible typographical error in the provided options.
Step-by-step explanation:
When determining the probability that Stephen Curry makes both free throws, given his shooting proportion is .908, we need to consider that the events are independent. We calculate the combined probability of two independent events by multiplying the probability of each event together. So the probability of making the first free throw is .908, and because the events are independent, the probability of making the second free throw is the same, .908.
To find the probability that he makes both free throws, we multiply the probability of the first event by the probability of the second event: .908 (first free throw) × .908 (second free throw) = .824464. None of the provided options exactly match this result; however, the closest one is Option 1: 0.827264, which should likely be the correct answer rounded to six decimal places. This indicates a possible typographical error in the calculation or in the options provided to the student.