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12-2 Conditional Probability 5/11/17 Conditional Probability: a type of probability that contains a condition which limits the sample space for an event. They are written P(B | A) and are read as “the probability of event B, given event A”. You will see some of these in chart form: Book classification at a local library Illustrated (I) Non- (NI) illustrated Hardback (H) 420 780 Nonfiction (NF) 590 250 Paperback Fiction (F) 150 (P) Nonfiction (NF) 110 430 Fiction (F) 880 What is the probability that a book selected at random is a paperback, given that it is illustrated? P(P | I) 260/1270 What is the probability that a book selected at random is nonfiction, given that it is a non-illustrated hardback? P(NF | NIH) 250/1030 A selection of Andrew McCutchen’s stats from 2012 & 2013. Find each conditional probability. P(HR | 2012 hit) = 31/194 P(2013 3B | 3B) = 5/11 2012 2013 Hits 194 185 2B 29 38 3B 6 5 HR 31 21 Some problems will be in word problem form, and it may appear that you have limited information. You can still answer questions about conditional probability using the Conditional Probability Formula Always the smaller chance. P(B | A) = P(A and B) P(A) The condition; the “given”. 80% of an airline’s flights depart on schedule. 72% of its flights depart and arrive on schedule. Find the probability that a flight that departs on time will also arrive on time. (P(A) is departure…) P(B | A) = .72 = .90 or 90% .80 P(B | A) = P(A and B) P(A) Let’s find the probability that McCutchen’s next hit is a 2B. In other words, the P(2B | Hit). P(2B | Hit) = P(Hit and 2B) P(Hit) As of 5/11/17 his P(Hit and 2B) is .0413 P(Hit) is .215 .0413 ÷ .215 = .1922 or about a 19% chance that his next hit is a 2B When using this formula, the smaller % always goes on top! Some problems will need to be solved with a tree diagram. Bo DeNardo, student of meteorology, makes the following observations: 28% of the time, the sky is “mostly clear” During the “mostly clear” days, it rained 4% of the time During the cloudy days, it rained 31% of the time .04 Rain .96 No rain Clear .28 .31 .72 Cloudy Rain What is the probability that a day will start out clear, but then it will rain? .28 • .04 = 1.12% or about 1% What is the probability that a day will be cloudy, but not rain? .72 • .69 = 49.68% or about 50% .69 No rain Page 644 #1 – 13, 19 – 22