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# Probability (Ch 13 & 14) STAT 2332

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## Popular in Introductory Statistics for Life Sciences

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This 4 page Class Notes was uploaded by veronica on Thursday October 6, 2016. The Class Notes belongs to STAT 2332 at University of Texas at Dallas taught by Dr. Chen in Fall 2016. Since its upload, it has received 44 views. For similar materials see Introductory Statistics for Life Sciences in Statistics at University of Texas at Dallas.

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Date Created: 10/06/16

Chapter 13 & 14: Probability NOTES Abbreviations and Key Words: “Ex:” short for Example, “w/” short for with, “#“ means number, P(something) means probability of ‘something’ “AKA” or “a.k.a.” short for Also Known As probability: describes chance of occurrence or outcome. P(event) = favorable outcome total outcomes sample space (S): collection of all possible outcomes. Represented w/ “S” Ex: roll a die S= {1,2,3,4,5} sample space Event: any collection of outcomes from the sample space. Represented w/ a letter (A, B, C, etc.) Ex: roll a die, Event A is rolling a prime # A= {2,3,5} Complement: the complement of an event is the event NOT occurring. S (sample space) Represented by A’ or Ā Ex: A= roll an even # A= {2,4,6} A Ā= do not roll an even # Ā= {1,3,5} A’ Complement Rule: (shaded part) P(A) + P(Ā) = 1 with replacement: in Ex: taking a card from a deck and putting it back without replacement: Ex: not putting the card back Conditional Probability: probability that takes into account a given condition; gives the probability of one event “given that” another event has happened. Notation is P(B|A) probability of B “given that” A has occurred; “Event B given Event A” *A is the 1 event and B is the 2 event. * P(B|A) = P(A and B) P(A) Conditional prob. equals P(A and B) divided by P(A) The above equation can be solved for P(A and B) which leads us to the multiplication rule. General Multiplication Rule P(A and B) = P(A) × P(B|A) a.k.a. P(1 and 2 ) = P(1 ) × P(2 |1 ) nd st *Use above equation for finding probabilities without replacement or when you have “given that” statements (conditional probability). ...if you have independent events, use P(A and B) = P(A) × P(B) *Use above equation for finding probabilities with replacement/independent events. Use this equation when proving two outcomes are independent; P(A and B) should equal P(A) times P(B) if independent. Independent: event has no effect on the probability of another event occurring. Ex: drawing with replacement Ex: In 3 tosses of a coin, what is the probability that you will get 3 tails (T)? P(T and T and T) = 0.5 × 0.5 × 0.5 = 1/8 or 0.125 The event A and B happens= consists of all outcomes that are in both events. Ex: A= drawing a red card A and B is the same as B= drawing a 3 A∩B aka intersection A and B = {2 hearts, 2 diamonds} A or B is the same as A∪B aka union P(A and B) = 2/52 cards = 1/26 The event A or B happens= consists of all outcomes that are in at least one of the 2 events. P(A or B) = P(A)+P(B)-P(A and B) Subtract Also called P(A and B) to avoid Addition Rule IF mutually exclusive: double counting P(A or B) = P(A)+P(B) mutually exclusive/disjoint: occurrence of one event prevents the occurrence of the other. Events cannot happen together at once. Ex: A= student is a freshman B= student is a sophomore Use addition rule for mutually exclusive events. P(A and B) = 0 or Ø (called an If P(A or B) equals P(A)+P(B) empty set, Ø means no outcomes) then events are mutually Ex: Toss coin 1 time. exclusive A= Head B=Tail P(A and B) = Ø Mutually exclusive events a.k.a. disjoint events will always have P(A and B) equal zero. Independent events are NOT the same thing as mutually exclusive events; independent events can happen at once. Mutually Exclusive Events Venn Diagram A B S P(at least one) = 1 – P(none) Thank you for reading my notes! Please look forward for more Reproduction/redistributing of these notes is not allowed.

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