Let (A_1) be the event that the form was checked by Clerk A1, and (A_2) be the event that the form was checked by Clerk A2.

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We are given:

[ P(A_1) = 0.55 ] (the probability that a form is checked by A1)

[ P(A_2) = 0.45 ] (the probability that a form is checked by A2)

[ P(\text{Error} | A_1) = 0.03 ] (the probability of error given A1 checked the form)

[ P(\text{Error} | A_2) = 0.02 ] (the probability of error given A2 checked the form)

We want to find (P(A_1 | \text{Error})) and (P(A_2 | \text{Error})).

Using Bayes’ Theorem:

[ P(A_1 | \text{Error}) = \frac{P(\text{Error} | A_1) \cdot P(A_1)}{P(\text{Error})} ]

[ P(A_2 | \text{Error}) = \frac{P(\text{Error} | A_2) \cdot P(A_2)}{P(\text{Error})} ]

Now, let’s find (P(\text{Error})):

[ P(\text{Error}) = P(\text{Error} | A_1) \cdot P(A_1) + P(\text{Error} | A_2) \cdot P(A_2) ]

Substitute the given values into the equations to find the probabilities.