Math Study Guide Chapter 4
Math Study Guide Chapter 4 Math M-118
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This 4 page Study Guide was uploaded by idk on Friday October 9, 2015. The Study Guide belongs to Math M-118 at Indiana University taught by George O'Donnell in Summer 2015. Since its upload, it has received 108 views. For similar materials see Finite Math in Mathematics (M) at Indiana University.
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Date Created: 10/09/15
Finite Math Chapter 4 Study Guide 41 Basic Concepts Probabilitya number expressing the likelihood that a specific event will occur expressed as the ratio of the number of actual occurrences to the number of possible occurrences An eventa collection of outcomes that is a subset of the sample space of an experiment Example An experiment is rolling a fair die An event of this experiment could be rolling an even number 246c123456 To find the probability of an event for an experiment that has equally likely outcomes we use the formula PrlEl nlEln5 This is the Basic Probability Formula If the problem involves sets we can draw a Venn diagram Odds in favor can be expressed as mn Odds against can be expressed as nm Formula PrEmmn 42 Conditional Probability Conditional probability is when we are asked to find the probability of an event occurring given that another event has already occurred PrAlB the bar is read as given B is the event we know happened the given event A is the event we want to find the probability of The given event is the conditional piece of the problem and forms the new sample space of the experiment the only set of outcomes we want to consider Formula PrAl BnAunion B nB This is the number of times both A and B can happened divided by the number of times B can happen the new sample space The quotandquot in the formula simply means that A and B both occurred It is not synonymous with multiplication Many times two events occur such that one event does not impact the likelihood of the other we say these events are independent if events are deemed to be independent then we have the following relationship PrAunion BPrAPrB we cannot use this formula when we don t know whether events A and B are independent using tree diagrams to solve these problems are very helpful in some cases 43 More Conditional Probability The order of the conditional question is ipped from the conditional questions in 42 Constructing a tree diagram and then using the conditional probability formula can solve problems like these Follow these steps to solve the problems 1 draw a tree diagram for the experiment 2 write question in conditional form 3 expand conditional using formula from 42 4 use the tree to solve the two problems 5 use calculator to evaluate final answer best if you round to 4 decimal places 44 Bernoulli Trials some multistage experiment satisfy a specific set of conditions which allows us to calculate probability in a special way These experiments are called Bernoulli Trials and can be soled using the binomial probability formula 1 must contain multiple stages 2 two possible outcomes success and failure 3 trials are independent 4 The probability of success is the same for each trial Formula Cnkpquotk1pquotnk N the number of trials of the experiment K the number of successes the question is asking for Pthe probability of success for each trial 1p the probability of failure for each trial These problems can be solved entirely by the use of the binomial probability formula and do not require Venns or trees
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