In a railway reservation office, two clerks are engaged in checking reservation forms. On an average, the first clerk (A1) checks 55% 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

To find the probabilities that the error in a randomly selected reservation form was checked by A1 and A2, we can use Bayes’ Theorem.

Get the full solved assignment PDF of MMPC-005 of 2023-24 session now.

Let’s denote the following:

P(A1) = Probability that a form was checked by clerk A1 = 0.55

P(A2) = Probability that a form was checked by clerk A2 = 0.45

P(Error|A1) = Probability of error given that A1 checked the form = 0.03

P(Error|A2) = Probability of error given that A2 checked the form = 0.02

We want to find P(A1|Error) and P(A2|Error), which are the probabilities that the error was checked by A1 and A2, respectively. We can use Bayes’ Theorem for this:

P(A1|Error) = (P(A1) * P(Error|A1)) / P(Error)

P(A2|Error) = (P(A2) * P(Error|A2)) / P(Error)

Now, let’s calculate P(Error):

P(Error) = P(A1) * P(Error|A1) + P(A2) * P(Error|A2)

P(Error) = (0.55 * 0.03) + (0.45 * 0.02)

Now, plug these values into the equations for P(A1|Error) and P(A2|Error):

P(A1|Error) = (0.55 * 0.03) / P(Error)

P(A2|Error) = (0.45 * 0.02) / P(Error)

Calculate P(Error) first, then use it to find P(A1|Error) and P(A2|Error). These will be the probabilities that the error was checked by A1 and A2, respectively.