Bayes' Rule - Law of Conditional Probability

A market research firms conducts studies regarding the success of new products. The company is not always perfect in predicting the success. Suppose that there is a 50% chance that any new product would be successful (and a 50% chance that it would fail). In the past, for all new products that ultimately were successful, 80% were predicted to be successful (and the other 20% were inaccurately predicted to be failures). Also, for all new products that were ultimately failures, 70% were predicted to be failures (and the other 30% were inaccurately predicted to be successes). What is the a priori probability that a new product would be a success?

a) 0.50
b) 0.80
c) 0.95
d) 0.70
e) 0.60

I don't understand how to do this problem. This uses Bayes' Rule. Can someone show the steps to do this? This is a problem in my textbook. No its not homework, its for my own studying.

• Hi and welcome to the site! I don't understand the question: You say that "there is a 50% chance that any new product would be successful" and in the end, the question asks "What is the a priori probability that a new product would be a success?". It seems to me that the question itself gives the answer. But where do the predictions come in? – COOLSerdash Sep 30 '13 at 18:01
• I don't get what the answer is. They give you answers but you gotta pick the right one as it is a multiple choice type question. Its to show your work and understand the process of reaching the answer. – user1757703 Sep 30 '13 at 23:29
• I presume there a couple of questions under this text and the first one "What is the a priori probability that a new product would be a success?" is only checking your understanding of the concepts. You do not need Bayes Rule for this, as others have pointed out, the answer P(Success) = 0.50 is in the question. – Zhubarb Oct 1 '13 at 16:01
• "its for my own studying" -- which thereby still falls under the self-study tag. Would you please add that tag? (NB It doesn't actually use Bayes' rule) – Glen_b Oct 1 '13 at 16:11