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?
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.