I am trying to do this question: The blood type distribution in the UK is: type A: $41\%$, type B: $9\%$, type AB: $4\%$, type O: $46\%$. It is estimated that every year, $4\%$ of patients with type O are classed as having type A, $88\%$ of those with type A are correctly classed as having type A, 4% with type B are classed as type A, and $10\%$ of those with type AB are classed as type A.
Now a patient is classed as having type A blood. What is the probability that this is his actual blood type (i.e. that he is correctly classed as having type A blood)?
But I am not sure what formula to use or how to even start on it. The course is currently going over Bayes theorem so I assume it is related to that but I do not see how that can be use here with this question. Can someone show what to do here?