Question

A medical test has a false positive rate of 0.2. If 9 tests are conducted, what is the chance of getting exactly 2 false positive results?

Answer 1

Answer on Question #44151, Math, Statistics and Probability

A medical test has a false positive rate of 0.2. If 9 tests are conducted, what is the chance of getting exactly 2 false positive results?

Solution.

Process follows the laws of the binomial distribution.

$$P_n(k) = C_k^n * p^k (1 - p)^{n-k}$$

Where $p$ is the probability of origin favorable events. $n$ is the number of samples. $k$ is the number of origin favorable events.

In this case:

$$P(2) = C_2^9 * 0.2^2 (1 - 0.2)^7 = \frac{9!}{7! \cdot 2!} \cdot 0.2^2 \cdot 0.8^7 \approx 0.3$$

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