The question goes like this:

It is know that 9% of the population belongs to blood group B.

How many people must a doctor - who is sampling random people - examine to be 99.8% confident of finding at least one person with blood group B?

\(\displaystyle P(X\geqx)\leq0.002\)

where X = the no. of people examined until someone with blood group B is found, therefore X has the distribution \(\displaystyle geom(\frac{91}{100}\))

\(\displaystyle \Rightarrow\log_{0.91}0.91^{(x-1)}\leq\log_{0.91}0.0002\)

\(\displaystyle \Rightarrow\(x-1)\leq65.9\) (using the log power rule on the LHS and 'de-logging' the RHS)

\(\displaystyle x\leq66.9\)

However, this should be \(\displaystyle x\geq66.9\) if the above statements are to hold true (and the question asks 'at least,' therefore a 'greater than or equal sign' must be in the final statement.)

Where have I gone wrong; I haven't divided or multiplied by negative numbers, unless unintentionally?

Thanks.

It is know that 9% of the population belongs to blood group B.

How many people must a doctor - who is sampling random people - examine to be 99.8% confident of finding at least one person with blood group B?

\(\displaystyle P(X\geqx)\leq0.002\)

where X = the no. of people examined until someone with blood group B is found, therefore X has the distribution \(\displaystyle geom(\frac{91}{100}\))

\(\displaystyle \Rightarrow\log_{0.91}0.91^{(x-1)}\leq\log_{0.91}0.0002\)

\(\displaystyle \Rightarrow\(x-1)\leq65.9\) (using the log power rule on the LHS and 'de-logging' the RHS)

\(\displaystyle x\leq66.9\)

However, this should be \(\displaystyle x\geq66.9\) if the above statements are to hold true (and the question asks 'at least,' therefore a 'greater than or equal sign' must be in the final statement.)

Where have I gone wrong; I haven't divided or multiplied by negative numbers, unless unintentionally?

Thanks.

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