Doctors

The drug successfully treats 90% of cases. Calculate the probability that it will cure at least 18 patients out of 20.

Correct answer:

P =  67.6927 %

Step-by-step explanation:

p=90%=10090​=109​=0.9  p18​=(1820​)⋅p18⋅(1−p)20−18=(1820​)⋅0.918⋅(1−0.9)20−18=190⋅0.918⋅0.12≐0.2852  p19​=(1920​)⋅p19⋅(1−p)20−19=(1920​)⋅0.919⋅(1−0.9)20−19=20⋅0.919⋅0.11≐0.2702  p20​=(2020​)⋅p20⋅(1−p)20−20=(2020​)⋅0.920⋅(1−0.9)20−20=1⋅0.920⋅0.10≐0.1216  P=100⋅ (p18​+p19​+p20​)=100⋅ (0.2852+0.2702+0.1216)=67.6927%

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