Question

in basketball, shaquille makes 40% of his free throw attempts. he goes to the free throw line to shoot one - and - one (if he makes the first shot, he gets to shoot one more). he scores 1 point per free throw. what is the expected value of the number of points he will score?

Explanation:

Step1: Calculate the probability of scoring 0 points

The probability of missing the first shot is \(1 - 0.4=0.6\). So the probability of scoring 0 points \(P(0)=0.6\).

Step2: Calculate the probability of scoring 1 point

The probability of making the first shot and missing the second shot is \(0.4\times(1 - 0.4)=0.4\times0.6 = 0.24\). So \(P(1)=0.24\).

Step3: Calculate the probability of scoring 2 points

The probability of making both shots is \(0.4\times0.4 = 0.16\). So \(P(2)=0.16\).

Step4: Calculate the expected value

The formula for expected value \(E(X)=\sum_{i}x_{i}P(x_{i})\). Here \(x_{0} = 0\), \(x_{1}=1\), \(x_{2}=2\).

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Answer:

\(0.56\)