the health department is developing a two stage procedure to relieve the symptoms of a rare blood disorder. The first procedure has a 70% probability of giving a person some relief(which is considered a success). If the first procedure does succeed, the second procedure has a 90% probability of success. If the first procedure does not succeed, the second procedure has only a 40% probability of success. What is the probability that:

Both procedure are successful? 70% x 90% = 63%

The first fails and the second succeeds? 30% x 40% = 12%

Both procedures fail? 30% x 60% = 18%

I believe all of the above are correct, but......

If you know the second procedure was successful, what is the probability tht the first procedure was successful? HELP please