1. Copyright © Texas Education Agency, 2012. All rights reserved. Basic Probability Facts Introduction Statistics & Risk Management 1 Copyright © Texas Education Agency, 2012. All rights reserved.

2. 2 “Copyright and Terms of Service Copyright © Texas Education Agency. The materials found on this website are copyrighted © and trademarked ™ as the property of the Texas Education Agency and may not be reproduced without the express written permission of the Texas Education Agency, except under the following conditions: 1)Texas public school districts, charter schools, and Education Service Centers may reproduce and use copies of the Materials and Related Materials for the districts’ and schools’ educational use without obtaining permission from the Texas Education Agency; 2) Residents of the state of Texas may reproduce and use copies of the Materials and Related Materials for individual personal use only without obtaining written permission of the Texas Education Agency; 3) Any portion reproduced must be reproduced in its entirety and remain unedited, unaltered and unchanged in any way; 4) No monetary charge can be made for the reproduced materials or any document containing them; however, a reasonable charge to cover only the cost of reproduction and distribution may be charged. Private entities or persons located in Texas that are not Texas public school districts or Texas charter schools or any entity, whether public or private, educational or non-educational, located outside the state of Texas MUST obtain written approval from the Texas Education Agency and will be required to enter into a license agreement that may involve the payment of a licensing fee or a royalty fee. Call TEA Copyrights with any questions you have.

3. 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

4. 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

5. 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

6. 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

7. 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

8. Events Independent Events Independent Events Mutually Exclusive Mutually Exclusive Exhaustive (No More) Exhaustive (No More) Copyright © Texas Education Agency, 2012. All rights reserved. 8

9. Geometry A point is selected at random in the RED/BLUE square. A point is selected at random in the RED/BLUE square. Calculate the probability that it lies in the BLUE triangle. Calculate the probability that it lies in the BLUE triangle. Midpoints p(b)=??????? Copyright © Texas Education Agency, 2012. All rights reserved. 9