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What is Probability? The probability of a random event denotes the relative frequency of occurrence of an experiment's outcome, when repeating the experiment. The probability of a random event denotes the relative frequency of occurrence of an experiment's outcome, when repeating the experiment. Frequentists consider probability to be the relative frequency "in the long run" of outcomes. Frequentists consider probability to be the relative frequency "in the long run" of outcomes. Copyright © Texas Education Agency, 2012. All rights reserved. 3

Why Probability? Probability theory is applied in everyday life in risk assessment and in trade on commodity markets, and the gaming industry. Probability theory is applied in everyday life in risk assessment and in trade on commodity markets, and the gaming industry. Governments typically apply probabilistic methods in environmental regulation, where it is called pathway analysis. Governments typically apply probabilistic methods in environmental regulation, where it is called pathway analysis. Copyright © Texas Education Agency, 2012. All rights reserved. 4

Analytical Method 100 M&Ms in a Bag 100 M&Ms in a Bag 24 Blue ones 24 Blue ones p(b)=24/(24b+76o)=.24 p(b)=24/(24b+76o)=.24 You have a.24 probability of randomly drawing out a Blue one. You have a.24 probability of randomly drawing out a Blue one. Copyright © Texas Education Agency, 2012. All rights reserved. 5

Probability to Odds 100 M&Ms in a Bag 100 M&Ms in a Bag 24 Blue ones. 24 Blue ones. p(b)=24/(24b+76o)=.24 p(b)=24/(24b+76o)=.24 You almost have odds of 1 in 4 of randomly drawing out a Blue one. You almost have odds of 1 in 4 of randomly drawing out a Blue one. Copyright © Texas Education Agency, 2012. All rights reserved. 6

Results p= 0.0 Not going to happen 0.0 Not going to happen 1.0 It will happen every time 1.0 It will happen every time ??? Somewhere in between ??? Somewhere in between Copyright © Texas Education Agency, 2012. All rights reserved. 7