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It is given that a combined blood sample of 36 people will test positive for HIV if at least one of the 36 samples tests positive.

One percent of the people in the world between the ages 15-49 years are positive for HIV.

Let Xdenote 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:

$$\begin{gathered} p=1\% \\ =\frac{1}{100} \\ =0.01 \end{gathered}$$

The probability of failure is computed below:

$$\begin{gathered} q=1-p \\ =1-0.01 \\ =0.99 \end{gathered}$$

The number of trials (n) is equal to 36.

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:

$$\begin{gathered} P\left(X猢�1\right)=1-P\left(X<1\right) \\ =1-P\left(X=0\right) \\ =1-{}^{36}{C}_0{\left(0.01\right)}^0{\left(0.99\right)}^{36-0} \\ =1-0.696413 \\ =0.304 \end{gathered}$$

Thus, the probability that the combined sample tests positive for HIV is equal to 0.304.

Since the value is not low, it is not unlikely for such a combined sample to test positive.