In a post office, three clerks are assigned to process incoming mail. The first clerk, A, processes 40 per cent; the second clerk, B, processes 35 per cent; and the third clerk, C, processes 25 per cent of the mail. The first clerk has an error rate of 0.04, the second has an error rate of 0.06, and the third has an error rate of 0.03. 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 A or clerk B or clerk C.
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Given : three clerks are assigned to process incoming mail.
l. The first clerk, A, processes 40 per cent
the second clerk, B, processes 35 per cent
he third clerk, C, processes 25 per cent of the mail.
The first clerk has an error rate of 0.04,
the second has an error rate of 0.06
the third has an error rate of 0.03.
A mail selected at random from a day’s output is found to have an error.
To Find : probability that it was processed by clerk A or clerk B or clerk C.
Solution:
Let say total mail = 10000
Processed by clerk A = (40/100) 10000 = 4000
Error = 4000 (0.04) = 160
Processed by clerk B = (35/100) 10000 = 3500
Error = 3500 (0.06) = 210
Processed by clerk C = (25/100) 10000 = 2500
Error = 2500 (0.03) = 75
Total Error = 160 + 210 + 75 = 445
probability that it was processed by clerk A = 160/445 = 32/89 = 0.36
probability that it was processed by clerk B = 210/445 = 42/89 = 0.47
probability that it was processed by clerk B = 75/445 = 15/89 = 0.17
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