Help with Bayes Theorem (possibly?) So let's suppose that there is a baseball player with a .300 batting average (i.e., the probability that he gets a hit is 30%) and he is facing a pitcher who has a .400 avg against (the probability that he gives up a hit is 40%). What would be the probability that this batter will get a hit off this pitcher? I tried to use Bayes theorem, but I got an answer of .222, which doesn't really make sense. Would the answer just be .350 (the average of the two), or is there some Bayesian way to get an answer?
 A: As @jlimahaverford said, there is not enough information. You are trying to determine 
$$ P(H|B=b,P=p) $$
where $H$ is the event "a hit", $B=b$ indicates the batter is $b$, and $P=p$ indicates the pitcher is $p$. But the information you have is 
$$ P(H|B=b) \quad \mbox{and} \quad P(H|P=p) $$
and there is no obvious way to get from these two pieces of information to what you are trying to determine.
One approach you might want to look into is logistic regression where the response is the binary outcome of each at bat (hit or no hit) and the explanatory variables are the IDs of the batter and hitter in that at bat. Then you could learn the quality of each batter and pitcher. From this information, you could predict what would happen for a particular batter-pitcher combination. 
A: As you stated your question, it's a bit ambiguous.  Based on my understanding of your question, it doesn't provide sufficient information to approach this problem in a Bayesian manner.
Suppose $A$ is the event that the batter succeeds, and $B$ is the event that the bowler fails.  You are given $p(A) = 0.3$ and $p(B) = 0.4$ and you are asked what $p(A|B)$ is.  Without any more information or constraints (i.e., whether $A$ depends on $B$ or not), the best you can say is $A$ is independent of $B$ and conclude that $p(A|B)=p(A)=0.3$.
