SOLUTION: A new surgery is successful 75% of the time. If the results of 7 such surgeries are randomly sampled, what is the probability that fewer than 5 of them are successful?
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Question 1079853: A new surgery is successful 75% of the time. If the results of 7 such surgeries are randomly sampled, what is the probability that fewer than 5 of them are successful? Answer by amfagge92(93) (Show Source):
You can put this solution on YOUR website! using binomial theorem.
P(X=x)=nCx.p^x.q^n-x
where n=7, p=0.25, q=0.75
P(X<5)=P(X≦4)=P(X=0)+P(X=1)+P(=2)+P(X=3)+P(X=4)
=0.1335+0.3115+0.3115+0.1730+0.0577=0.9872
alternatively
P(X<5)=1-P(X≧4)
P(X≧4)=P(X=5)+P(X=6)+P(X=7)
=0.0128
P(X<5)=1-P(X≧4)
∴1-0.0128
0.9872.
