Question

g Assuming the probability of a single sample testing positive is 0.15​, find the probability of a positive result for two samples combined into one mixture. Is the probability low enough so that further testing of the individual samples is rarely​ necessary?

Answer 1

Solution :

The objective is to obtain the $\text{probability of a positive result}$ for 2 samples combined into a $\text{mixture}$.

Given that the $\text{probability of a single sample testing positive is 0.15}$

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))

                                  $= 1-P(-ve )^2$

                                  $=1-[1-P(+ve)]^2$

                                  $=1-(1-0.15)^2$

                                  $=1-(0.85)^2$

                                  = 1 - 0.7225

                                  = 0.2775

No, the probability is not low enough.