Final answer:
The probability of basketball player Marta making at least 2 out of 3 free throw attempts, given she has a 90% success rate for each independent shot, requires combining the probabilities of her making exactly 2 and exactly 3 free throws.
Step-by-step explanation:
The question is asking for the probability that Marta, a basketball player who makes 90% of her free throws, will make at least 2 out of 3 attempts. Since the results of each free throw are independent, we can calculate the probability of making 2 or 3 shots directly.
To calculate the probability of making exactly 2 free throws, we consider the 3 possible ways this can happen (MMF, MFM, FMM) where 'M' represents a made shot and 'F' a failed shot. Each of these has a probability of 0.9 × 0.9 × 0.1 due to independence. We then consider the probability of making all 3 free throws, which is 0.9 × 0.9 × 0.9.
The total probability of making at least 2 free throws is the sum of these two cases. So we calculate it as P(X ≥ 2) = 3 × (0.9 × 0.9 × 0.1) + (0.9 × 0.9 × 0.9). Calculating gives us the final answer.