Probability of malaria

A survey at a hospital indicates that the probability of a patient testing positive for malaria is 0.6. Two patients are selected at random. What is the probability that:
(i) one tests negative and the other tests positive?
(ii) both patients test positive?

Final Answer:

p₁ =  0.48
p₂ =  0.36

Step-by-step explanation:

$$\begin{gathered} p=0.6 \\ {C}_1(2)=\left(\genfrac{}{}{0ex}{}{2}{1}\right)=\frac{2!}{1!(2-1)!}=\frac{2}{1}=2 \\ {p}_1=\left(\genfrac{}{}{0ex}{}{2}{1}\right)\cdot p\cdot (1-p)=2\cdot 0.6\cdot (1-0.6)=0.48 \end{gathered}$$

$p_2=p^2=0.6^2=0.36$

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