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Unformatted text preview: Probability and Statistics Probability and Statistics Probability and Statistics Devore and Devore and Berk Berk Chapter 2 Chapter 2 What is the chance of an event happening? • Winning the toss of a coin? • Getting 4 aces in 5 card poker hand? • Having blue eyes if one parent has blue and the other brown? • Surviving from age 1 to age 2 if you’re a sardine? Sample Space and Events • Sample Space – Set of all possible outcomes • Event – Subset of S – Grouped by some set of characteristics • Space={Cards}, Event={Aces} S Sample Space Event A Mutually Exclusive Events Space={Cards}, Events= A {Aces} B {Kings} P(A)=P(B) S Sample Space Event A Event B Probability = Area Space={Cards}, Events= A {Tens} B {Face Cards} P(B) > P(A) S Sample Space Event A Event B Events that are Not Mutually Exclusive Space={Cards}, Events= A {Aces} B {Hearts} • Union • A B • Intersection • A B • Conditional • P(AB) = P(A B)/P(B) S Sample Space Event A Event B I U I Events that are Not Mutually Exclusive • Conditional • P(AB) = P(A B)/P(B) P(ace given it’s a heart) = P(ace of heart)/ P(heart) = 1/52 / 13/52 = 1/13 S Sample Space Event A Event B I Addition Rule • Probability that A or B or both occur • P(A or B) = P(A) + P(B) – P(A and B) Event B Event A S Sample Space Addition Rule • Probability of getting an ace or a heart is • P(Ace) + P(Heart) – P(Ace of hearts) • 4/52 + 13/52 – 1/52 = 16/52 Event A Event B Enumerate the Possibilities • Combin ator ics – Counting, arranging, ordering Permutation with Repetition License Plates • How many license plates can be made using 3 letters and then 3 numbers? • E x a m p l e : A B C 1 2 3 26 x 26 x 26 x 10 x 10 x 10 = 17,576,000 Permutation without Repetition Jumble • Arrangement of objects where order matters. • JUMBLE game in Ithaca Times • Clue Answer • Artifa ct LEIR C RELIC Permutation Notation • R E L I C 5 l e t t e r s • 5 ways to choose first letter • 4 ways to choose second • a n d s o o n … • 5x4x3x2x1 = 120 • 5! factorial(5) • 1 2 Make Your Own JUMBLE • sample(c("R","E","L","I","C")) • "I" "C" "L" "R" "E" • sample(c("R","E","L","I","C")) • "L" "I" "E" "C" "R“ • Random izat ion Combination Coin Tosses • Components of a group important, but not their arrangement....
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This note was uploaded on 11/12/2009 for the course BTRY 3010 at Cornell.
 '07
 SULLIVAN,P.

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