A basketball player makes 80% of her free throws. Assuming each attempt is independent, what is the probability that she makes exactly 3 of her next 4 free throws?

Step 1: Recognize the binomial setting.

There are 4 independent attempts, each attempt has two outcomes, and the probability of success remains 0.80.

Use the binomial probability formula:
P(X = k) = C(n,k)p^k(1-p)^(n-k)

Step 2: Identify the values.

n = 4
k = 3
p = 0.80
1 - p = 0.20

Step 3: Substitute into the formula.

P(X = 3) = C(4,3)(0.80)^3(0.20)^1

Step 4: Evaluate the combination.

C(4,3) = 4

So:
P(X = 3) = 4(0.80)^3(0.20)

Step 5: Evaluate the powers and multiply.

(0.80)^3 = 0.512

P(X = 3) = 4(0.512)(0.20)
P(X = 3) = 0.4096

Therefore, the probability that she makes exactly 3 of the 4 free throws is 0.4096, or 40.96%.