# probability of success

• May 27th 2010, 06:48 PM
EAWyman
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
• May 27th 2010, 10:06 PM
downthesun01
Quote:

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:

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