Question

Marta makes 90 ?

1) 80
2) 90
3) 100
4) 110
Marta makes 90% of the free throws she attempts. she is going to shoot 3 free throws. assume that the results of free throws are independent from each other. let x represent the number of free throws she makes. find the probability that marta makes at least 2 of the 3 free throws. you may round your answer to the nearest hundredth. p(xgeq2)=?

Answer 1

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.