In a blood testing procedure blood samples from 6 people are

In a blood testing procedure, blood samples from 6 people are combined into one mixture. The mixture will only test negative if all the individual samples are negative.If the probability that an individual sample tests positive is 0.1, what is the probability that the mixture will test positive?

Solution

The probability that individual test negative is

P(individual tests negative)= 1-0.1=0.9

The probability that all individuals test negtaive is

P(all individuals tests negative)= (0.9)*(0.9)*(0.9)*(0.9)*(0.9)*(0.9)=0.5314

The mixture will test positive if at least one individual test will be positive. So the probability that the mixture will test positive is

P(mixture will test positive) =1 - P(all individuals tests negative)= 1- 0.5314=0.4686