Question

In a railway reservation office, two clerks are engaged in checking reservation forms. On an average, the first clerk (A1) checks 55 per cent of the forms, while the second (A2) checks the remaining. While A1 has an error rate of 0.03 that of A2 is 0.02. A reservation form is selected at random from the total number of forms checked during a day and is discovered to have an error. Find the probabilities that it was checked by A1, and A2, respectively.

Answer 1

Probability that a form is checked by A1 = 0.55      and by A2 = 0.45

Error rate of A1 = 0.03          A1 checks 97 forms out of a 100 correctly.
Error rate of A2 = 0.02          A2 cheks 98 forms out of a 100 corectly.

Probability that a form is checked by A1 and also correctly: 0.55 * 0.97 = 0.5335
Probability that a form is checked by A1 and wrongly : 0.55 * 0.03 = 0.0165

Probability that a form is checked by A2 and also correctly: 0.45*0.98 = 0.4410
Probability that a form is checked by A2 and wrongly : 0.45 * 0.02 = 0.0090

These events are exclusive and independent.

We have a form that has an error. Probability that it is checked

by A1 :  0.0165 / (0.0165 + 0.0090) = 0.6471  or  64.71%

by A2 : 0.0090 / (0.0165 + 0.0090) =  0.3529 or 35.29%

Answer 2

This is done by bayes theorem and from this theorem we can find the probability in different ways