What we need here is P[at least 2 misses] = 1 - P[no miss] - P[player A misses 1] - P[player B misses 1]
True. Of course, if we are looking at this set of possibilities, it's easier to calculate the probability of nobody missing anything and subtracting from 1:
P[at least 1 miss] = 1 - P[no miss] = 1 - [2C2*p1*p1][2C2*p2*p2] = 1 - [(1)(0.825)(0.825)][(1)(0.796)(0.796)] = 1 - 0.431 = 0.569
So yeah, the probability was pretty good someone was going to miss something.
What we need here is P[at least 2 misses] = 1 - P[no miss] - P[player A misses 1] - P[player B misses 1]
nerd alert!
Rewrite this as P[at least 2 misses] = 1 - P[no miss] - P[player A misses 1, player B makes both] - P[player A makes both, player B misses 1]
1 - 0.431 - 0.183 - 0.221 = 0.165
Definitely not betting odds...
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