Study Ch. 4.2, # 41(37), 48(39), 53(41), 57(45), 55(43), 59(47) Class Notes: Prof. G. Battaly, Westchester Community College, NY. Event.

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1 GOALS: 1. Use Venn Diagrams to help understand which individuals in population have certain characteristics. 2. Understand differences between events having both conditions and events having either condition. Study Ch. 4.2, # 41(37), 48(39), 53(41), 57(45), 55(43), 59(47) : Prof., Westchester Community College, NY Sample Space: collection of all possible outcomes Event: collection of outcomes with specified characteristic; subset of sample space Sample Space E Event not E not E: complement of E outside E, inside sample space : Prof., Westchester Community College, NY

2 Suppose have two events, A and B How many regions in each sample space? A B Regions Regions : Prof., Westchester Community College, NY Suppose have two events, A and B How many regions in each sample space? A B Regions Regions Note: If region 3 is empty, then the right one is essentially the same as the left. : Prof., Westchester Community College, NY

3 Shade (A & B) in both A and B Shade (A or B) in either A or B or both : Prof., Westchester Community College, NY Shade (A & B) in both A and B Shade (A or B) in either A or B or both : Prof., Westchester Community College, NY

4 A B coffee (A) or tea (B) : Prof., Westchester Community College, NY : Prof., Westchester Community College, NY

5 Eastcoast: NYG, NE, BA, M, NYJ, TB Northeast: NE, NYG, NYJ Events, Mutually Exclusive Events What about the events * being a team on the east coast and * being a team in the northeast? Are these events M.E.? : Prof., Westchester Community College, NY p DA SF GB NYG NE W BA DE M OA CH IN KC LA NO NYJ ST TB What about the events > being a team on the east coast and >being a team in the northeast? M.E.? : Prof., Westchester Community College, NY

6 A B What about the events > being a team on the east coast and >being a team in the northeast? M.E.? P KC GB DA W NO M A NE B BA NYG TB DE NYJ LA ST SF IN OA CH : Prof., Westchester Community College, NY What about the events > being a team on the east coast and >being a team in the northeast? M.E.? Eastcoast: NYG, NE, BA, M, NYJ, TB Northeast: NE, NYG, NYJ : Prof., Westchester Community College, NY

7 Toss a dime four times. How many possible outcomes are there? What are the possibilities? 1st 2nd 3rd 4th toss 2 x 2 x 2 x 2 = 16 possible outcomes : Prof., Westchester Community College, NY Toss a dime four times. How many possible outcomes are there? What are the possibilities? 1st 2nd 3rd 4th toss 2 x 2 x 2 x 2 = 16 possible outcomes Two possible outcomes for each toss. There are 4 tosses, so: Number of possible outcomes = Here ORDER matters, since HHTT is a different outcome from HTHT and THTH, etc. NOT n C r where order does not matter and HHTT is same as HTHT, etc. : Prof., Westchester Community College, NY

8 HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT p. 159 # 44, 48 THHH THHT THTH THTT TTHH TTHT TTTH TTTT Event A: exactly 2 heads Event B: first 2 tosses are tails Event C: first toss is heads Event D: all 4 tosses are the same : Prof., Westchester Community College, NY HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT p. 159 # 44, 48 THHH THHT THTH THTT TTHH TTHT TTTH TTTT Event A: exactly 2 heads Event B: first 2 tosses are tails Event C: first toss is heads Event D: all 4 tosses are the same : Prof., Westchester Community College, NY

9 P(M or TB)? F: probablility that a Super Bowl team selected at random is either Miami or Tampa Bay. Seattle Seahawks 1 Philadelphia Eagles 1 : Prof., Westchester Community College, NY P(M or TB)? ME, so no overlap, simply add. (If there is overlap, then not ME and need to be careful not to count the overlap twice.) : Prof., Westchester Community College, NY

10 Addendum: Need to update: 2013 Baltimore Ravens 2014 Seattle Seahawks 2015 NE Patriots 2016 Denver Broncos 2017 NE Patriots 2018 Philadelphia Eagles