I know generally conditional probability questions are presented in the form: "What is the probability of Event A given Event B," and from there it can be written as:
$P(A|B)$
However, how is that determined when the question doesn't explicitly state the given condition?
For example, if we have a question such as, "What is the probability that a randomly selected baseball player is a pitcher who voted "Yes" on the team questionnaire?"
Would it be
$P($Pitcher | Voted Yes$)$
or
$P($Voted Yes| Pitcher$)$
Thank you!
Best Answer
It's neither. For conditional probability you assume that one event happened, and then ask for the probability that an additional event also happened. Here, you aren't assuming either event. Here you are asked for $P(\text {Pitcher}\cap \text {Voted Yes})$
Conditional statements would be, for instance, "Given that the player you selected voted Yes, what is the probability that you selected a Pitcher?" or "Given that the player you selected was a Pitcher, what is the probability that he voted Yes?".