Question

In a post office, three clerks are assigned to process incoming mail. The first clerk A, processes
38 per cent; the second Clerk B, processes 33 per cent; and the third clerk C, process 29 per cent of the mail.
The first clerk has an error rate of 0.035, the second has an error rate of 0.055, and the third has an error rate
of 0.035. A mail selected at random from a day's output is found to have an error. The postmaster wishes to
know the probability that it was processed by clerk B?​

Answer 1

Given : In a post office, three clerks are assigned to process incoming mail.

The first clerk A, processes 38 per cent;

the second Clerk B, processes 33 per cent;

the third clerk C, process 29 per cent of the mail.

The first clerk has an error rate of 0.035,

the second has an error rate of 0.055,

the third has an error rate of 0.035.

A mail selected at random from a day's output is found to have an error.

To Find :  the probability that it was processed by clerk B?​

Solution  

the first clerk  A checks 38 % of the forms

error rate of 0.035

Chances of error = 0.38*0.035 = 0.01330

second clerk  B checks  33% of the forms

error rate of 0.055

Chances of error = 0.33 * 0.055 = 0.01815

Third clerk  C checks  29% of the forms

error rate of 0.035

Chances of error = 0.29 * 0.035 = 0.01015

A reservation form is selected at random from the total number of forms checked during a day, and is found to have an error

probability that it was checked by the second clerk B  =0.01815 /( 0.01330 + 0.01815 +0.01015 )  = 1815/4160

= 363/832

= 0.4363

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