Solving problem N3703 Bayesian probability theory

Solving problem N3703 Bayesian probability theory

3703. Two typists typed on the same number of pages. The probability that the first typist makes a mistake is 0.3; the second is 0.2. Randomly selected page. Find the probability that:
1) there is an error on the selected page;
2) the mistake was made by the first typist.

Additional information:

Detailed solution. Decorated in Microsoft Word 2003 (Quest decided to use the formula editor)