A commitee is formed by randomly selecting from eight nurses and two doctors. What is the minimum commitee size that ensures at least a 90% probablity that it will not be comprised of nurses only?

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aruv | High School Teacher | (Level 2) Valedictorian

Posted on

Let committee is formed by selecting only nurse and size of the committee be x.

E= allmembers in committee are nurse.

`barE=` all members in committee are not nurse






By given condition,






Either  `x<=(19+sqrt(37))/2 and x>=(19-sqrt(37))/2`

`=> 6.45(approx)<=x<=12.54 (approx)`


`x>=(19+sqrt(37))/2 and x<=(19-sqrt(37))/2`

`` which  has no solution.

Thus size of committee may either 7 or 8 or 9 or 10.