How do I get either conditional or joint probabilities if I'm given the prior...

#1
How do I get either the conditional and joint probabilities if I'm given the prior and posterior probabilities.

I'm doing a decision analysis that requires the application of Baye's law.

I have the following information:


s1=.2 P(s1|F)=.7
s2=.8 P(s2|F)=.3
...that's for the favorable side

s1=.2 P(s1|U)=.2
s2=.8 P(s2|U)=.8
...that's for the unfavorable side

From this information, how could I get the both the conditional and joint probabilities? Is it possible?
 
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#2
Actually, I think it would be better to post the question asked:

Tommy is a film producer evaluating a new film proposal by Jason Kim, a rookie screenwriter and director. Tommy knows that the probability of a film by a new screenwriter being successful is only 20%, with the probability of a film being a flop being 80%. A successful film will earn the studio a profit of $50 million and a flop will lose $20 million.

Jenny would like to hire a noted film critic, Mike Taylor, to read the script and assess the film's chances of success. In the past, Taylor has been able to predict a successful film 70% of the time and correctly predict an unsuccessful film 80% of the time.


They want me to select the optimal decision. I don't know whether I interpreted the question right or wrong but from by understanding of the additional information, they have provided the posterior probabilities. Am I mistaken?