Question 1185670
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Medical billing errors and fraud are on the rise. According to the MBAA website, 8 out of 10 times, 
the medical bills that you get are not right. If a sample of 10 medical bills is selected, what is the probability that
a. 0 medical bills will contain errors?
b. Exactly 5 medical bills will contain errors?
c. More than 5 medical bills will contain errors?
d. What are the mean and standard deviation of the probability distribution
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        In the post by  @CPhill,  all calculations in part  (c)  are incorrect.

        I came to provide correct calculations.



<pre>
**c. More than 5 medical bills will contain errors:**

This means we need to find the probability of 6, 7, 8, 9, or 10 bills containing errors and add them together. 
It's often easier to use the complement rule:


    P(x > 5) = 1 - [P(0) + P(1) + P(2) + P(3) + P(4) + P(5)]


Calculating each of these probabilities and summing them, then subtracting from 1, will give you P(x > 5).  
Due to the small probability of P(0) and P(1), we can ignore the results of P(0), P(1)


    P(2) = (10C2) * (0.8)^2 * (0.2)^8 =  45 * 0.8^2 * 0.2^8 ≈ 7.3728E-05

    P(3) = (10C3) * (0.8)^3 * (0.2)^7 = 120 * 0.8^3 * 0.2^7 ≈ 0.000786432

    P(4) = (10C4) * (0.8)^4 * (0.2)^6 = 210 * 0.8^4 * 0.2^6 ≈ 0.005505024

    P(5) = (10C5) * (0.8)^5 * (0.2)^5 = 252 * 0.8^5 * 0.2^5 ≈ 0.026424115


    P(x > 5) = 1 - (7.3728E-05 + 0.000786432 + 0.005505024 + 0.264] ≈ 0.9672.   <U>correct ANSWER to (c)</U>
</pre>

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If it is an Artificial Intelligence, then how it may happen
that elementary arithmetic calculations are incorrect ?


I do not believe to my eyes . . .