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Intro and Addition Rule Notes Spring

Intro and Addition Rule Notes Spring - 2 of 10 DEFINITIONS...

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2 of 10 1.1 Fundamentals DEFINITIONS Rare event rule. Definition 1.1 If we observe an event that has an small probability of being observed, we conclude that our assumptions about its probability are wrong . It wasn’t random chance. (Very Important!) Example 1 . In 1986, the official estimated probability (via modeling) of the shuttle failing was 1/1,000. That year we observed the Challenger Shuttle mission fail. Event: A, B, C . Definition 1.2 An outcome or result of a procedure. Example 2 (Event) . Rolling a die (the procedure) and getting a 4 (the event). Compliment of an event: ¯ A, ¯ B, ¯ C . Definition 1.3 All outcomes in which an event does not occur. Example 3 (Compliment of an event) . Then the compliment of getting a 4 on a die roll is not getting a 4 (or getting a 1, 2, 3, 5, 6). Simple event. Definition 1.4 An event that cannot be broken down into simpler events. Compound event. Definition 1.5 An event that combines two or more simple events. Example 4 (Compound event) . Roll two dice (the procedure) and get sum of 8 (the event). Example 5 (Simple event) . Roll two dice (the procedure) and get a { 4, 4 } .

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