where the letters are for the following 
p probabilitya event ab event bunconditional probability is also known as marginal probability and measures the chance of something happening while ignoring any knowledge of previous or external events since this probability also ignores new information it remains constant examples of conditional probabilityan example of conditional probability using marbles is illustrated below the steps are as follows step 1 understand the scenarioinitially you re given a bag with six red marbles three blue marbles and one green marble thus there are 10 marbles in the bag step 2 identify the eventsnext two events are defined step 3 calculate the probability of event b p b event b is drawing a marble that is not green there are 10 marbles altogether nine of which are not green the six red and three blue marbles p b n u m b e r o f m a r b l e s t h a t a r e n o t g r e e n t o t a l n u m b e r o f m a r b l e s 9 10 p b number of marbles that are not green total number of marbles 9 10 p b numberofmarblesthatarenotgreen totalnumberofmarbles 9 10step 4 identify the intersection of events a and b p a b the intersection of events a and b involves drawing a red marble that is also not green since all red marbles are not green the intersection is simple the event of drawing a red marble step 5 calculate the probability of the intersection of events a and b p a b p a b n u m b e r o f r e d m a r b l e s t o t a l n u m b e r o f m a r b l e s 6 10 3 5 p a b number of red marbles total number of marbles 6 10 3 5 p a b numberofredmarbles totalnumberofmarbles 6 10 3 5step 6 calculate the conditional probability p a b using the conditional probability formula p a b that is the probability of drawing a red marble given that the marble drawn is not green the probability is calculated p a b p a b p b 3 5 9 10 2 3 p a b p a b p b 3 5 9 10 2 3 p a b p a b p b 3 5 9 10 2 3the conditional probability of drawing a red marble given that the marble drawn is not green is 2 3 let s practice with another example of conditional probability using a fair die the steps are as follows step 1 understand the scenarioyou have a fair six sided die you want to determine the probability of rolling an even number given that the number rolled is greater than four step 2 identify the eventsthe possible outcomes sample space for a six sided die are the numbers one through six from this list you can define the two events step 3 calculate the probability of each eventthe probability of each event can be calculated by dividing the number of favorable outcomes the ones you re looking for by the total number of outcomes in the sample space p a is the probability of rolling an even number there are three even numbers 2 4 6 out of the six possible outcomes thus p a 3 6 1 2 p b is the probability of rolling a number greater than four two numbers are greater than four 5 6 out of the six possible outcomes thus p b 4 6 2 3 step 4 identify the intersection of events a and bthe intersection of events a and b includes the outcomes that satisfy both conditions simultaneously in this case that means rolling a number that is even and also greater than four the only outcome that does both is rolling a six step 5 calculate the probability of the intersection of events a and bwe ll spell this out even if it s easy given the above because other examples might prove more difficult p a b is the probability of rolling six since six is the only outcome that is both even and greater than six there is one outcome out of six possibilities so p a b 1 6 step 6 calculate the conditional probability p b a the formula for conditional probability is as follows p b a p a b p a p b a p a b p a p b a p a b p a 