Many companies today have a mandatory drug testing policy for their employees. To minimize the cost of testing, sample from 6 people are combined. If the mixture tests negative then all 6 individual employees are also negative. Find the probabilty of a positive result for 6 samples combined into 1 mixture assuming the probability of a individual sample testing positive is 0.01
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To find the probability of a positive result for the combined mixture, we can use the concept of complementary probability.
The probability that the mixture tests negative is equal to the probability that all individual samples test negative.
Since the probability of an individual sample testing positive is 0.01, the probability of an individual sample testing negative would be 1 - 0.01 = 0.99.
Therefore, the probability that all 6 individual samples test negative is 0.99 raised to the power of 6 (0.99^6).
To find the probability of a positive result for the mixture, we need to subtract the probability of the mixture testing negative from 1.
So, the probability of a positive result for the combined samples is 1 - 0.99^6.
Calculating this, we have:
1 - 0.99^6 = 1 - 0.941480149 = 0.058519851
Therefore, the probability of a positive result for the 6 samples combined into 1 mixture is approximately 0.0585 or 5.85%.