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? 0.064 0.24 0.56 0.80 done

Explanation:

Step1: Calculate 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 is $P(0)=0.6$.

Step2: Calculate probability of scoring 1 point

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

Step3: Calculate probability of scoring 2 points

The probability of making both shots is $0.4\times0.4=0.16$.

Step4: Calculate expected value

The expected - value formula is $E(X)=\sum_{i}x_{i}P(x_{i})$. Here, $x_0 = 0$, $x_1 = 1$, $x_2 = 2$, $P(0)=0.6$, $P(1)=0.24$, $P(2)=0.16$. So $E(X)=0\times0.6 + 1\times0.24+2\times0.16=0.24 + 0.32=0.56$.

Answer:

0.56