# Math Help - probability of success

1. ## probability of success

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

2. Originally Posted by EAWyman
If you know the second procedure was successful, what is the probability tht the first procedure was successful? HELP please
You can use Bayes' Theorem

$pr(A|B)=\frac{pr(B|A)pr(A)}{pr(B|A)pr(A)+pr(B|A')p r(A')}$

Let A=the first procedure was successful, let B= the second procedure was successful

From the information you gave we know:

$pr(A)=0.7$
$pr(A')=0.3$
$pr(B|A')=0.4$
$pr(B|A)=0.9$