Conditional Probability

Conditional ProbabilitySometimes our computation of the Probability of an eventis changed by the knowledge that a related event hasoccurred (or is guaranteed to occur) or by some additionalconditions imposed on the example, based on a .292 batting average for 2016, wemight assign Probability 29% to Kris Bryant having a hit inhis first at-bat of suppose (closer to opening day), we learn that thepitcher Bryant will be facing in his first at-bat will beleft-handed. We might want to (indeed we should) use thisnew information to re-assign the ProbabilityBased on the data that Bryant had a .314 batting averageagainst left-handed pitching in 2016, we might now assignprobability 31% to him having a hit in his first at-bat new Probability is referred to as aconditionalprobability, because we have someprior informationabout conditions under which the experiment will information may change thesample spaceand thesuccessful event ProbabilityExampleLet us consider the following experiment: Acard is drawn at random from a standard deck of that there are 13 hearts, 13 diamonds, 13 spades and13 clubs

blue marbles, I draw a marble at random from the bag and then, without replacing the rst marble, I draw a second marble. What is the probability that both marbles are red? We can draw a tree diagram to represent the possible outcomes of the above experiment and label it with the

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  Probability, Ambler, Conditional, Conditional probability

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