# Find the probability that a restaurant Ramsay visits remains open for another year given they implement his advice?

Gordon Ramsay gives advice to the owners of failing restaurants. He then revisits each of the restaurants one year later to see if they are still open, and talks to the employees. Ramsay finds that among the restaurants that are still open, 95% implemented his advice, and among the restaurants that closed, only 50% implemented his advice. Further, most of the restaurants visited were in pretty bad shape financially, so assume only 40% would have been able to survive another year.

Thus, use Bayes Rule to find P(O|A), the probability a restaurant Ramsay visits remains open for another year, given that they implement his advice.

I really have no idea where to start with this one. I tried to begin it with plotting a tree diagram but the percentages just aren't adding up correctly so any help would be appreciated.

• Do you know what Bayes' rule is? What does it have to do with this problem? – saulspatz Feb 15 at 0:47
• I am learning about bayes' rule although I think its suffice to say I'm still learing how to use it, however the part of the question stating to use bayes rule is a part of the question not something I added in. – mad Feb 15 at 0:50
• I'm not suggesting that the problem has nothing to do with Bayes' rule; I'm suggesting you try to figure out how Bayes' rule applies. Start by writing down Bayes' rule, and then try to apply it. – saulspatz Feb 15 at 0:52