This question is in continuation to: Obtaining binomial distribution from normal distribution, and repeated events.
Let us consider a random variable, $x$ chosen from a normal distribution. Define, $x \leq 4$ as event A. We are given with pdf of occurrence of a second event B, $P(B/A)$. Literally, event B here indicates whether the player has lost or not. It is imminent, the probability of occurrence of B relies on the state of event A. The question is to calculate the expected total loss. However, I am confused about whether to use conditional, Baysean probability, $P(A/B)$, or $P(A \cap B)$ to calculate expectation.
N.B.: Literally, In a cricket match, event A is one of the possible moves taken up by the fielding team (in a cricket match). The batsman has a set of moves, and, batsman's strategy relies on the move taken up by the fielding team. Say, $B$ is the set of moves that beats him (or, incurs some cost $\mathcal{C}$), i.e., $P(B/A)$ is known. $\mathcal{C}$ is a constant. I need to calculate the expected number of times the batsman is lost and the incurred cost.