Final answer:
The probability that Helen makes both free throws is found by multiplying the probability of making the first shot with the conditional probability of making the second shot given the first one is made, which results in a probability of 63.75%.
Step-by-step explanation:
The subject of the question pertains to probability in mathematics, which involves predicting the outcome of an event where there are several possible outcomes. In this scenario, Helen has a probability of 75% or 0.75 to make a free throw shot in basketball. We are given P(C) = 0.75 for the first shot and P(D) = 0.75 for the second shot. Moreover, it is specified that Helen’s probability to make the second free throw given that she made the first is 0.85. To find the probability of Helen making both free throws, we can multiply the two probabilities together:
P(C and D) = P(C) × P(D|C),
where P(D|C) is the probability of making the second shot given the first one was made.
Substituting the values, we can calculate:
P(C and D) = 0.75 × 0.85,
P(C and D) = 0.6375.
Therefore, the probability that Helen makes both free throws is 0.6375, which can also be expressed as 63.75%.