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Stats 309 6-1 to 6-2

Stats 309 6-1 to 6-2 - 6.1 Assigning Probabilities to...

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6.1 Assigning Probabilities to Events Random experiment – process or course of action that results in one of a number of possible outcomes. The outcome cannot be predicted. ie – the flip of a coin, roll of a die To determine the probability that a particular outcome will occur, we first need to know all possible outcomes. List them! Sample space – a list of all possible outcomes, usually denoted with an S = {O 1 , O 2 , … , O n } Simple events – individual outcomes O 1 , O 2 ,… Event – a collection of one or more simple events For example : If our experiment is rolling a die: the sample space S = {1,2,3,4,5,6} If Event A is defined to be an even number then A = {2,4,6} Ultimately we want to find the probability that an event happens, P(A). The probability of Event A is equal to the sum of the probabilities assigned to the simple events contained in A. P(A) = P(2) + P(4) + P(6)
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Requirements of Probabilities If E i represents the simple events, so S = {O 1 , O 2 ,…, O n } then: = = n i i i O P i O P 1 1 ) ( ) 2 each for 1 ) ( 0 ) 1 The probability of any outcome must lie between 0 and 1, inclusive. The sum of the probabilities of all the outcomes in a sample space must be 1.
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Example Flip a coin twice S = {HH, HT, TH, TT} Four simple events, each event equally likely, so each simple event has a probability of ¼. Warning!!!! You won’t always have experiments where each simple event is equally likely. Each of the events in this problem is equally likely because, with a fair coin, H and T are equally likely. When
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