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?
The probability that an individual sample tests negative is 1 - 0.1 = 0.9.
Since the mixture will only test negative if all the individual samples are negative, the probability that the mixture will test negative is (0.9)^6 = 0.531441.
Therefore, the probability that the mixture will test positive is 1 - 0.531441 = 0.468559. Answer: \boxed{0.468559}.
To find the probability that the mixture will test positive, we need to find the probability that at least one individual sample tests positive.
Let's calculate the probability that an individual sample tests negative. Since the probability that an individual sample tests positive is 0.1, the probability that it tests negative is 1 - 0.1 = 0.9.
For the mixture to test negative, all individual samples must test negative. Therefore, the probability that the mixture will test negative is (0.9)^6 = 0.531441.
The probability that the mixture will test positive is 1 - probability of testing negative = 1 - 0.531441 = 0.468559.
So, the probability that the mixture will test positive is approximately 0.468559, or 46.86%.
To solve this problem, we need to use the concept of complementary probability.
The probability that an individual sample tests positive is 0.1. Therefore, the probability that an individual sample tests negative is 1 - 0.1 = 0.9.
Since all individual samples need to test negative for the mixture to test negative, we can calculate the probability that the mixture will test negative by multiplying the probabilities of all 6 individuals testing negative together.
The probability of the mixture testing negative = (0.9) * (0.9) * (0.9) * (0.9) * (0.9) * (0.9) = (0.9)^6.
To find the probability that the mixture will test positive, we subtract the probability of the mixture testing negative from 1.
Probability of the mixture testing positive = 1 - (0.9)^6.
Now we can calculate the probability.
Probability of the mixture testing positive = 1 - (0.9)^6
= 1 - 0.531441
= 0.468559
Therefore, the probability that the mixture will test positive is approximately 0.4686, or 46.86%.