During the NCAA basketball tournament season, affectionately called March Madness, part of one team's strategy is to foul their opponent if his free-throw shooting percentage is lower than his two-point field goal percentage. Jeff's free-throw shooting percentage is lower and is only $57.1 \%$. After being fouled he gets two free-throw shots each worth one point. Calculate the expected value of the number of points Jeff makes when he shoots two free-throw shots.

Step 1 ：During the NCAA basketball tournament season, affectionately called March Madness, part of one team's strategy is to foul their opponent if his free-throw shooting percentage is lower than his two-point field goal percentage. Jeff's free-throw shooting percentage is lower and is only \(57.1 \%\). After being fouled he gets two free-throw shots each worth one point. We are asked to calculate the expected value of the number of points Jeff makes when he shoots two free-throw shots.

Step 2 ：The expected value of a random variable is the sum of the probability of each outcome times the value of each outcome. In this case, the random variable is the number of points Jeff makes when he shoots two free-throw shots. There are three possible outcomes: he makes both shots (2 points), he makes one shot (1 point), or he makes no shots (0 points). The probability of each outcome depends on Jeff's free-throw shooting percentage, which is \(57.1 \%\) or \(0.571\).

Step 3 ：Let's denote the probability of making a shot as \(p_{make}\) and the probability of missing a shot as \(p_{miss}\). We have \(p_{make} = 0.571\) and \(p_{miss} = 1 - p_{make} = 0.429\).

Step 4 ：The expected value is calculated as follows: \(expected\_value = 2*p_{make}^2 + 1*2*p_{make}*p_{miss} + 0*p_{miss}^2 = 1.142\).

Step 5 ：This means that on average, Jeff is expected to make 1.142 points every time he shoots two free-throw shots.

Step 6 ：Final Answer: The expected value of the number of points Jeff makes when he shoots two free-throw shots is \(\boxed{1.142}\).