conditional probability is used when two or more events are not independent this means the likelihood of one event is influenced by whether another event occurred it asks if we know a has happened what s the chance of b also happening it s calculated by multiplying the probability of the preceding event by the updated probability of the succeeding or conditional event we ll walk you through the calculation below 
conditional probability can be contrasted with unconditional probability the latter is also called marginal probability which measures the chance of a single event without depending on any other in contrast conditional probability determines the likelihood of one event given that another event has occurred linking them other terms for probabilities include independent probability which doesn t have that interconnectedness and instead looks at the probability of some event in isolation because it s believed to be independent a joint probability is the likelihood of two events occurring together from these ideas one can get to bayes theorem which provides a way to flip conditional probabilities mathematically if you know the chance of event b happening given event a bayes formula lets you reverse calculate the conditional probability of a given b overall while marginal and joint probabilities measure individual and paired events conditional probability can measure precedence and dependence between events understanding conditional probabilityconditional probabilities are contingent on a previous event it measures the likelihood of an event or outcome based on the occurrence of some earlier event two events are said to be independent if one event occurring does not affect the probability that the other event will occur however if one event occurring or not does affect the likelihood that the other event will happen the two events are said to be dependent for example a company s stock price increasing after reporting higher than expected earnings if events are independent then the probability of some event b is not contingent on what happens with event a for example an increase in apple s shares and a drop in wheat prices conditional probability is often written as the probability of a given b and notated as p a b conditional probability is used in a variety of fields such as insurance economics politics and different fields of mathematics conditional probability formulap b a p a a n d b p a p b a p a and b p a p b a p aandb p a or p b a p a b p a p b a p a b p a p b a p a b p a 