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

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.