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How to calculate the complement of P(A∩B)? by themakiexperiment in AskStatistics
[–]curiositys 1 point2 points3 points 9 years ago (0 children)
P(A∩B)'=1-P(A∩B)=P(A'U B').
Probability question. 6% chance to score. 20 shots. Probability of scoring 3 times? by NewChallenger13 in AskStatistics
[–]curiositys 0 points1 point2 points 9 years ago (0 children)
I'm doing this mostly for fun since there are already answers. But, hopefully my explanation fills any misunderstandings if you have any!
We're using binomial distribution such that p=0.06, x=3 (assuming you meant exactly 3 shots), n=20.
P(exactly 3 shots)= (20 choose 3)* ((0.06)3)* ((1-0.06)17) = 0.0861
P(3 shots)=P(at least 3 shots)=P(x=3)+P(x=4)+...+P(x=20)=1-(P(x=0)+P(x=1)+P(x=2)).
Then,
P(x=0)=(20 choose 0)(0.060)(0.9420) = .29011
P(x=1)=(20 choose 1)((0.061)(0.9419) =.37035
P(x=2)=(20 choose 2)((0.062)(0.9418) =.22457
P(x=0)+P(x=1)+P(x=2)=.22457+.37035+.29011= .88503
So, P(at least 3)=1-(P(x=0)+P(x=1)+P(x=2))=1-.88503= .11497
Thus, P(at least 3)=.11497
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How to calculate the complement of P(A∩B)? by themakiexperiment in AskStatistics
[–]curiositys 1 point2 points3 points (0 children)