Find the indicated probability Round to the nearest thousand

Find the indicated probability. Round to the nearest thousandth. 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 0.11, what is the probability that the mixture will test positive?

Solution

The mixture will test negative if all the individual samples are negative

p = Prob for an individual sample test positive =0.11

Each person is independent and there are two outcomes hence X no of persons testing positive is binomial

Sample size =6

Prob mixture test is positive

= P(X>=1)

= 0.5030