91Ó°ÊÓ

It is given that a combined blood sample of 8women will test positive for anemia if at least one of the eight samples tests positive.

Ten percent of women aged 65 and above are positive for anemia.

Let X denote the number of samples that test positive in the combined sample.

Success is defined as getting a positive sample in the combined sample.

The probability of success is computed below:

$$\begin{gathered} p=10\% \\ =\frac{10}{100} \\ =0.1 \end{gathered}$$

The probability of failure is computed below:

$$\begin{gathered} q=1-p \\ =1-0.10 \\ =0.90 \end{gathered}$$

The number of trials (n) is equal to 8.

The binomial probability formula is as follows:

$P\left(X=x\right)={}^n{C}_x{\left(p\right)}^x{\left(q\right)}^{n-x}$

By using the binomial probability formula, the probability of at least one positive sample is computed below:

$$\begin{gathered} P\left(Xâ\copyright ¾1\right)=1-P\left(X<1\right) \\ =1-P\left(X=0\right) \\ =1-{}^8{C}_0{\left(0.10\right)}^0{\left(0.90\right)}^{8-0} \\ =1-0.430467 \\ =0.570 \end{gathered}$$

Thus, the probability that the combined sample tests positive for anemia is equal to 0.570.

Since the value is quite high (greater than 50%), it is likely for such a combined sample to test positive for anemia.