Probability 30271

The probability of an adverse drug reaction is 2.1%. How many people need to be prescribed for one patient to experience side effects with a chance of 90%?

Correct answer:

n =  0

Step-by-step explanation:

q=2.1%=1002.1​=0.021 p2​=90%=10090​=109​=0.9  p2​ = (1n​)⋅ q1⋅ (1−q) n−1 p2​ = n⋅ q⋅ (1−q) n−1  0.9 = n⋅ 0.021⋅ (1−0.021) n−1 0.9 = n⋅ 0.021⋅ (1−0.021) n−1 42.857 = n ⋅  0.979 n−1  C1​(10)=(110​)=1!(10−1)!10!​=110​=10  p10​=(110​)⋅ q1⋅ (1−q)(10−1)=10⋅ 0.0211⋅ (1−0.021)(10−1)≐0.1735 C1​(100)=(1100​)=1!(100−1)!100!​=1100​=100  p100​=(1100​)⋅ q1⋅ (1−q)(100−1)=100⋅ 0.0211⋅ (1−0.021)(100−1)≐0.2569 C1​(200)=(1200​)=1!(200−1)!200!​=1200​=200  p200​=(1200​)⋅ q1⋅ (1−q)(200−1)=200⋅ 0.0211⋅ (1−0.021)(200−1)≐0.0615 C1​(1000)=(11000​)=1!(1000−1)!1000!​=11000​=1000  p1000​=(11000​)⋅ q1⋅ (1−q)1000−1=1000⋅ 0.0211⋅ (1−0.021)1000−1=1.3006⋅10−8  n=0

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