Math Lecture Notes Week 7
Math Lecture Notes Week 7 MATH 105-02
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This 3 page Class Notes was uploaded by Danielle Kelly on Friday February 27, 2015. The Class Notes belongs to MATH 105-02 at Washington State University taught by Spencer Payton in Spring2015. Since its upload, it has received 68 views. For similar materials see Exploring Mathematics in Mathematics (M) at Washington State University.
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Date Created: 02/27/15
Math 105 21232127 Chapter 11 Basic Concepts Deterministic Phenomenon Something you can know 100 Example 5bs of peaches 89c per pound 589 445 for 5bs of peaches Random Phenomenon Can t know with 100 accuracy Example Number of peaches a produce manager should order customer demand Probability Measure of likelihood An observation or measurement of a random phenomenon is an experiment 0 Outcome possible results of experiment 0 Flipping a coin the outcomes would be heads or tails Sample space set of all possible outcomes Event subset of the sample space Success outcome that belongs to an event quotfavorable outcomequot S Sample space E event Success is contained in E failure is not S Example IF a single coin is tossed nd the probability that it will land heads up Heads and tails are equally ikey Experiment tossing a single fair coin Sample space HT Event Heads up EH Probability of heads up PE12 Theoretically Example If a Styrofoam cup is tossed nd the probability that I will land top down Outcomes are NOT equally ikey 1 Tossed cup 50 times 2 landed on its side 44 times 3 landed on its top 5 times 4 Landed on its bottom 1 time ii PtOP 50 10 Key This is experimentally not theoretically Theoretical Probability All outcomes in the sample space S are equally likely E event in the sample space total PE Zof favorable outcomes Z n of outccomes 6 2 115 Empirical Probability E event that may happen when the experiment performed Lof gtltE occured Z of Xexperiment was performed PE February 27 2015 Example Find the probability of being dealt each of the owing hands in vecard poker a A full house 3 cards of one numbers and two of another house 13C1 X 4C3X 12C1X 4C2 ways of poker cards 52C5 2598960 3744 6 Pfu housel 25989604165 000144058 b A royal ush ace king queen jack and ten of one suit of royal ush s 4 4 1 Proya39 USh 2598960 2 649740 z 000000154 These above are theoretical problems Example In 2006 there were 1482 million males and 1528 million females in the United States If we randomly select someone from that population that year what is the probability that that person is male Empirical problem Lof males 1482million Pma Ie total population 1482 million1528 million z 0492 Law of large Numbers The more you repeat an experiment the close the empirical probability will be to the theoretical probability Odds If all outcomes in a sample space are equally likely A of them are favorable to event E and the remaining B outcomes are unfavorable to E then the odd in favor of E are A to B and the odds against E are B to A A Total of outcomes PE AB Example Bob bought 12 raf e tickets to win an iPad If 104 tickets were sold and each has an equal chance of winning what are the odds against Bob39s winning the iPad He has 12 chances to win and has 92 chances to lose Odds against 92 to 12 9212 or 233 Converting between probability and odds Let E be an event X 1 If PE then the odds in favor of E are x to yx Odds against yx to x 2 If the odds in favor of E are A to B 61 Then PE ab Example If there are a 30 chance of rain tomorrow what are the odds in favor and odds against i 3 PE 100 T 10 39 Odds in favor 3 to 1037 37 Odds against 73 Examples Your odds in favor of winning a sweepstakes are 199999 What is the probability you will win 1 1 2000001 PWln 199999 100000
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