Question

In order to verify the accuracy of their financial accounts, companies use auditors on a regular basis to verify accounting entries. The company's employees make erroneous entries 5% of the time. Suppose that an auditor randomly checks three entries.

(a) Find the probability distribution for X , the number of errors detected by the  auditor.

(b) Find the probability that the auditor will detect more than one error.

 

Answer 1

Solution

(a) Find the probability distribution for X , the number of errors detected by the auditor

\( X\sim Bin(3,0.05) \hspace{2mm} , P=0.05 \)

so , \( P(X=x)=C_n^xP^x\left(1-P\right)^{n-x}\hspace{2mm},n=3 \)

                         \( =C_3^1P^x\left(1-P\right)^{3-x} \)

Then \( P(X=0)=(1-P)^3=(1-0.05)^3=0.857375 \)

         \( P(X=1)=3\times 0.05\times (1-0.05)^3=0.135375 \)

         \( P(X=2)=3\times(0.05)^2\times (1-0.05)=0.007125 \)

         \( P(X=3)=(0.05)^3=0.000125 \)

(b) Find the probability that the auditor will detect more than one error.

\( \implies P(X>1)=P(X=2)+P(X=3)=0.007125+0.000125=0.00712 \)

Therefore.

a).

b). \( P(X>1)=0.00712 \)