SOLUTION: Dr. Zivkov has developed a new procedure that he believes can correct a life-threatening medical condition. If the success rate for this procedure is 40 % and the procedure is trie

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Question 1203054: Dr. Zivkov has developed a new procedure that he believes can correct a life-threatening medical condition. If the success rate for this procedure is 40 % and the procedure is tried on 8 patients, what is the probability that at least 2 of them will show improvement?
The probability is:
(Round your answer to 3 decimal places.)
Answer by ikleyn(52874) About Me  (Show Source):
You can put this solution on YOUR website!
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Dr. Zivkov has developed a new procedure that highlight%28cross%28he%29%29 highlight%28cross%28believes%29%29 can correct a life-threatening
medical condition. If the success rate for this procedure is 40 % and the procedure is
tried on 8 patients, what is the probability that at least 2 of them will show improvement?
~~~~~~~~~~~~~~~~~ 

It is a typical problem on binomial distribution probability.

The number of trials is n= 8; 
the probability of success of each individual trial is p= 0.4;
the successful trials indexes are 2 or 3 or 4 or 5 or 6 or 7 or 8 patients


    So,  P = P(2) + P(3) + P(4) + P(5) + P(6) + P(7) + P(8).


Having so many calculations to do, it is better (more economic and more efficient way) 
to transform the formula equivalently

      P = 1 - P(0) - P(1) = 1+-+C%5B8%5D%5E0%2A0.4%5E0%2A%281-0.4%29%5E8+-+C%5B8%5D%5E1%2A0.4%5E1%2A%281-0.4%29%5E7 = 

        = 1+-+1%2A1%2A0.6%5E8+-+8%2A0.4%5E1%2A0.6%5E7 = 0.8936  (rounded).    ANSWER

Solved.