Answer:
There is a 34.39% probability of a positive result for four samples combined into one mixture.
This probability is not low enough so that further testing of the individual samples is rarely necessary,
Step-by-step explanation:
There are only two possible outcomes. Either a sample tests positive, or it does not, so we use the binomial probability distribution.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinatios of x objects from a set of n elements, given by the following formula.
And is the probability of X happening.
A number of sucesses x is considered unusually low if and unusually high if
In this problem, we have that:
There are four samples, so
Each sample has a probability of 0.1 of being positive, so .
Assuming the probability of a single sample testing positive is 0.1, find the probability of a positive result for four samples combined into one mixture.
If any sample is positive, the result of the four samples is positive. So this is . Either the number of positive samples is 0, or it is greater than 0. The sum of the probabilities is decimal 1. So:
In which
There is a 34.39% probability of a positive result for four samples combined into one mixture.
This probability if larger than 5%, so it is not low enough so that further testing of the individual samples is rarely necessary.