Conditional Probability

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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 ProbabilityExampleL

Calculating Conditional Probabilities (b) What is the probability that the day chosen was a Sunny day, P(S)? The sample space is still the 30 days under discussion. It was sunny on 9 + 1 = 10 of them so P(S) = 10 30 ˇ33%. (c) What is P G S? P G S = P(G\S) P(S). Hence we need to calculate P(G\S). Here the sample space is still

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