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A certified public accountant (CPA) has found that nine of
Chapter 3, Problem 73E(choose chapter or problem)
A certified public accountant (CPA) has found that nine of ten company audits contain substantial errors. If the CPA audits a series of company accounts, what is the probability that the first account containing substantial errors
a is the third one to be audited?
b will occur on or after the third audited account?
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QUESTION:
A certified public accountant (CPA) has found that nine of ten company audits contain substantial errors. If the CPA audits a series of company accounts, what is the probability that the first account containing substantial errors
a is the third one to be audited?
b will occur on or after the third audited account?
ANSWER:Step 1 of 3
Let X be the number of the company accounts which containing substantial errors.
Given
The Probability that an account contains substantial error (Probability of success),
\(\begin{aligned}
\mathrm{P} & =\frac{9}{10} \\
& =0.9
\end{aligned}\)
\(\Rightarrow\) Probability that an account does not contains substantial error,
\(\begin{aligned}
\mathrm{q} & =1-\mathrm{p} . \\
& =1-0.9 \\
& =0.1
\end{aligned}\)
So we can say that, X follows the geometric distribution with probability of success 0.9.
Thus, the probability density function of X:
\(\mathrm{P}(\mathrm{x})=q^{x-1} p, \mathrm{x}=1,2,3 . .\)
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