SOLUTION: a commitee is formed by randomly selecting from eight nurses and two doctors. what is the minimum commitee size that ensures at least 90% probabaility that it will be compromised o

Algebra ->  Probability-and-statistics -> SOLUTION: a commitee is formed by randomly selecting from eight nurses and two doctors. what is the minimum commitee size that ensures at least 90% probabaility that it will be compromised o      Log On


   

Question 202836: a commitee is formed by randomly selecting from eight nurses and two doctors. what is the minimum commitee size that ensures at least 90% probabaility that it will be compromised of nurses only?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
I could be wrong because Probability is not a strength for me. But I think the answer is that it is impossible to achieve at least 90% probability that a committee of only nurses will be chosen.Here's why:
  • If the committee size is 1 then the probability of all nurses is 8/10 0r 80%.
  • If the committe size is two, then the probability of all nurses is (8/10)*(7/9) which is less than 80%.
  • Since we need to increase the chances of all nurses to achieve 90% we would have to, at some point, multiply the initial 80% by a number greater than 1. But probabilities are never greater than 1.
  • So a committee of 1 with a probability of 80% is the closest we could ever get to 90%.