Read my post again.
At the outset before the shots are taken, a 70% FT shooter is more likely to make both shots (49%) than making just one shot (42%) or missing both (9%).
You are adding miss one and miss both together...you cannot do that as both cannot happen at the same time.. There are 4 (3 distinct) separate outcomes in this one particular situation. The most likely outcome given the 3 distinct possibilities is the player making both shots, making fouling inadvisable.
Now if you repeat the situation enough times, you are correct that it will end up that the player will make either one shot or miss both 1% more often than the player making both.
But in any one individual trip to the foul line, a 70% free throw shooter is more likely to make both free throws than not make them.
maybe im misunderstanding.. these are the situations written out
7 (made first shot)
----3 (made first, missed second (21)
---7 (made first, made second (49)
3 (missed first)
----7 missed first, made second) (21)
----3 missed first, missed second(9)
there is a cumulative 51 percent chance that we both agree on, that you miss the first and make the second, miss the first and the second, or make the first but miss the second... that cumulative 51 percent has a diversified set of outcomes but it is still more probable, collectively, that one of these three scenarios will happen instead of making both
i dont understand how youre saying the ultimately most likely scenario is one that doesnt beat the summation of alternative scenarios in probability of happening..
if I have 3 blue socks, 1 red, 1 black, 1 orange, 1 yellow, 1 maroon, 1 white, its likely im not pulling out a blue sock from a hamper if im blind folded..
"a 70% FT shooter is more likely to make both shots (49%) than making just one shot (42%) or missing both (9%)"
right, its not outcome 1 vs outcome 2 OR outcome three, its outcome 1 vs. outcome 2 AND outcome three