Respuesta :
Solution :
The objective is to obtain the [tex]\text{probability of a positive result}[/tex] for 2 samples combined into a [tex]\text{mixture}[/tex].
Given that the [tex]\text{probability of a single sample testing positive is 0.15}[/tex]
The probability of the positive test result is calculated as follows :
P ( positive mixture ) = P(1 or more samples positive)
                 = 1 - P (none +ve)
                 = 1 - P ((-ve) x (-ve))
                 [tex]$= 1-P(-ve )^2$[/tex]
                 [tex]$=1-[1-P(+ve)]^2$[/tex]
                 [tex]$=1-(1-0.15)^2$[/tex]
                 [tex]$=1-(0.85)^2$[/tex]
                 = 1 - 0.7225
                 = 0.2775
No, the probability is not low enough.
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