It is observed that there will be 25 blood specimens of normal persons, if 100 blood samples are tested. If…

It is observed that there will be 25 blood specimens of normal persons, if 100 blood samples are tested. If 10 specimens are sent to a laboratory for testing, then the probability of having at least two specimens of normal persons is
  1. $1-\frac{13}{4}\left(\frac{3}{4}\right)^{10}$
  2. $1-\frac{13}{4}\left(\frac{3}{4}\right)^9$
  3. $1-10\left(\frac{3}{4}\right)^{10}$
  4. $1-\left(\frac{3}{4}\right)^{10}-10\left(\frac{3}{4}\right)^9 \frac{1}{4}-45\left(\frac{3}{4}\right)^8\left(\frac{1}{4}\right)^2$

Solution

The probability of selecting a normal specimen from a pool of 100 blood samples is $\frac{25}{100}=\frac{1}{4}$ $ \therefore \mathrm{P}=\frac{1}{4} $ $ q=1-\frac{1}{4}=\frac{3}{4} $ No. of trials $=\mathrm{n}=10$ $ \begin{aligned} & P(x \geq 2)=1-P(x < 2) \\ & =1-P(x=1)-P(x=0) \\ & =1-{ }^{10} C_1\left(\frac{1}{4}\right)^1\left(\frac{3}{4}\right)^9-{ }^{10} C_0\left(\frac{1}{4}\right)^0\left(\frac{3}{4}\right)^{10} \\ & =1-\frac{13}{4}\left(\frac{3}{9}\right)^9 \\ & \therefore P(x \geq 2)=1-\frac{13}{4}\left(\frac{3}{9}\right)^9 \end{aligned} $

Asked in: AP EAMCET 2023 (18 May Shift 2)

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