expected value hack-a-shaq problem I am having trouble feeling confident i got the right answer here. i am not sure about the free throw calculation. my initial feelings were to do 80*.466 + 40*.466 + 0*.466 for the expected value of free throws vs. field goals which i calculated as 80*.596. Am i doing the calculations right? what is the right answer here? 
Problem:
Imagine you are a high school basketball coach and the opposing team has a very tall
and athletic player named Shaquille O’Beal. “Baby Shaq” (as he is known) is so good that
players on other teams have lots of diculty stopping him from scoring once he catches a
pass. Indeed, throughout the high school season he made 59.4% of the shots he took.
2
In basketball,when a player trying to make a shot is hit on the body by someone on the
opposing team, thereby causing the player to miss the shot, the player gets to take two free
shots from 15 feet away from the basket. These shots are called “foul shots.”
Like his namesake, “Baby Shaq” does not shoot foul shots very well.In fact, he makes only
46.6% of his foul shots. Regular shots are worth two points. Foul shots are worth one point
each. Because Shaq is less likely to make foul shots, one strategy is to foul him whenever
he touches the ball. This strategy has been nicknamed the ”hack-a-BabyShaq” plan (i.e.
intentionally fouling BabyShaq). Let’s see if - given the data - the Hack-A-BabyShaq is
actually a sound approach.
Please Evaluate whether the “Hack-a-BabyShaq” plan is sound. In doing so, please make
specific reference to the expected number of points that are generated using “Hack-a-
BabyShaq” plan versus not fouling Baby Shaq. For simplicity sake, assume that Baby
Shaq takes 40 shots per game and that in each instance your players could foul BabyShaq
before he could actually shoot his shot (i.e. assume “3 point plays” are not possible).
 A: The probabilities for the free throws were not calculated correctly. The probabilities of getting $2$ points, $1$ point, and $0$ points are not $0.466$.  
The probability Baby hits two free throws (gets $2$ points) is $(0.466)^2$.
Now let us calculate the probability Baby gets exactly one free throw, that is, gets $1$ point. This is the probability of hit then miss, plus the probability of miss then hit. Each of these has probability $(0.466)(0.534)$. Double. We get $0.497688$.
The probability Baby gets $0$ points on the free throws could be calculated, it is $(0.534)^2$, but irrelevant for the calculation of the mean.
Now calculate as you did, but with the modified probabilities.
Note: We assumed independence, which may not be realistic.
Remark: We used roughly the same idea as yours, just corrected the probabilities. The approach described by Ross Millikan is much better, in that it involves minimal calculation. As a bonus, it does not require independence. 
A: The way the problem is set, you don't care how many shots BabyShaq will take-all you care about is the expected score each time he gets the ball.  Your options are to let him shoot or to foul. In real life, you might have to worry about players fouling out, resulting in the other opponents scoring at will, but that is not part of the problem.  Given that, your choice is to let him shoot-what is the expected score for that?  Or you can foul him-he get two foul shots-what is the expected score of that?  Take your pick, because each incident is independent, so you can use the linearity of expectation.
