Question 1042175: Explain how a value such as one of those in the table could be used to find the
chances of Yao Ming making 0, 1, or 2 of 2 successive field goals, assuming the 2 field goals are independent, and a possible reason why 2 field goals might not be independent.
Table: https://s32.postimg.org/qcengm1r9/math.png
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! In an ideal world, any two events would be independent. However, if Yao Ming is on a hot streak hitting many shots in a row, then the probability of making the next shot is probably going to be larger than normal. This is because there is a mental/psychological aspect to the game. Also, it could work in the other way: if Yao Ming keeps missing a shot, then the probability could be smaller than normal.
The table can be used to compute the probabilities of hitting exactly 0 shots, exactly 1 shot, or exactly 2 shots using the binomial distribution theorem. The value of p would be drawn from the table and each event would be assumed to be independent. While this isn't necessarily true in the real world, it's still a fairly good approximation.
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