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# 4 6 Probablitiy

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### 4 6 Probablitiy

1. 1. Review of Probability and Statistics Algebra I Chapter 4.3
2. 2. Math Warm-Up <ul><li>Write each decimal as a fraction and percent. </li></ul><ul><li>3 / 4 </li></ul><ul><li>7/10 </li></ul><ul><li>2/9 </li></ul><ul><li>125/300 </li></ul><ul><li>.75 or 75% </li></ul><ul><li>.70 or 70% </li></ul><ul><li>.222 or 22.2% </li></ul><ul><li>5/12=0.417 or 41.7% </li></ul>
3. 3. Probability answers the question: How likely will the event occur?
4. 4. Probability <ul><li>Can be measured from 0 – 100% </li></ul><ul><li>Most often is measured in fractions. </li></ul>
5. 5. Experimental vs. Theoretical Probability
6. 6. Experiments <ul><li>Are done many times </li></ul><ul><li>Can sometimes have unexpected results </li></ul><ul><li>Sometimes work the way you expect them to. </li></ul><ul><li>Related to science and math </li></ul>
7. 7. Theory <ul><li>Expectations </li></ul><ul><li>Potential results </li></ul>
8. 8. Experimental Probability <ul><li>Shake dice and count how many of each number </li></ul><ul><li>Spin a spinner and count how many times it falls on red, blue, or green </li></ul><ul><li>Flip a coin and record the results. </li></ul>
9. 9. Theoretical Probability <ul><li>Use the number of possible outcomes divided by the total number of outcomes. </li></ul><ul><li>Count </li></ul><ul><li>Predict </li></ul>
10. 10. How may possible outcomes? <ul><li>How many times could an even number be rolled? </li></ul>3 out of 6
11. 11. 3 out of 6 <ul><li>As a fraction: </li></ul><ul><li>One chance in every two is the theoretical probability of rolling an even number. </li></ul>
12. 12. P (4)= <ul><li>How many fours on one cube? </li></ul><ul><li>… out of how many numbers on a rolling cube? </li></ul><ul><li>1/6 </li></ul>
13. 13. Sample set <ul><li>Two Coins </li></ul><ul><li>H, H </li></ul><ul><li>H, T </li></ul><ul><li>T, H </li></ul><ul><li>T, T </li></ul>
14. 14. Sample set <ul><li>Three Coins </li></ul><ul><li>H, H, H </li></ul><ul><li>H, H, T </li></ul><ul><li>H, T, T </li></ul><ul><li>H, T, H </li></ul><ul><li>T, H, H </li></ul><ul><li>T, H, T </li></ul><ul><li>T. T. H </li></ul><ul><li>T, T. T </li></ul>
15. 15. P (1h and 1t) =? <ul><li>Matching outcomes (h,t) (t,h) </li></ul><ul><li>Two chances in four </li></ul><ul><li>1 chance in every two. </li></ul><ul><li>50 % = ½ </li></ul>
16. 16. Sample Set Two Dice <ul><li>( 1, 1); ( 1, 2); ( 1, 3); ( 1, 4); ( 1, 5); ( 1, 6) </li></ul><ul><li>( 2, 1); ( 2, 2); ( 2, 3); ( 2, 4); ( 2, 5); ( 2, 6) </li></ul><ul><li>( 3, 1); ( 3, 2); ( 3, 3); ( 3, 4); ( 3, 5); ( 3, 6) </li></ul><ul><li>( 4, 1); ( 4, 2); ( 4, 3); ( 4, 4); ( 4, 5); ( 4, 6) </li></ul><ul><li>( 5, 1); ( 5, 2); ( 5, 3); ( 5, 4); ( 5, 5); ( 5, 6) </li></ul><ul><li>( 6, 1); ( 6, 2); ( 6, 3); ( 6, 4); ( 6, 5); ( 6, 6) </li></ul>
17. 17. <ul><li>( 1, 1); ( 1, 2); ( 1, 3); ( 1, 4); ( 1, 5); ( 1, 6) </li></ul><ul><li>( 2, 1); ( 2, 2); ( 2, 3); ( 2, 4); ( 2, 5); ( 2, 6) </li></ul><ul><li>( 3, 1); ( 3, 2); ( 3, 3); ( 3, 4); ( 3, 5); ( 3, 6) </li></ul><ul><li>( 4, 1); ( 4, 2); ( 4, 3); ( 4, 4); ( 4, 5); ( 4, 6) </li></ul><ul><li>( 5, 1); ( 5, 2); ( 5, 3); ( 5, 4); ( 5, 5); ( 5, 6) </li></ul><ul><li>( 6, 1); ( 6, 2); ( 6, 3); ( 6, 4); ( 6, 5); ( 6, 6) </li></ul><ul><li>What is the probability of shaking a one? </li></ul><ul><li>What is the probability of shaking doubles? </li></ul><ul><li>p (even, even) = </li></ul><ul><li>p (3, odd) = </li></ul><ul><li>p (odd, odd) = </li></ul><ul><li>p (even, even) = </li></ul><ul><li>p (total >5) = </li></ul><ul><li>p (total < 7) = </li></ul>Use two dice
18. 18. 6 red buttons and 3 blue buttons
19. 19. 9 buttons are placed into a bag What is the chance of blindly drawing a red button?
20. 20. Six favorable outcomes out of nine buttons
21. 21. From the bag <ul><li>What is the chance of pulling out a blue button? </li></ul><ul><li>3 out of 9 </li></ul>
22. 22. When figuring theoretical probability <ul><li>Find the number of favorable outcomes </li></ul><ul><li>Find the number of possible outcomes </li></ul><ul><li>Make a fraction. </li></ul><ul><li>Put the fraction in lowest terms </li></ul><ul><li>Divide for the decimal </li></ul><ul><li>Move 2 places for % </li></ul>
23. 23. Assignment <ul><li>Pg 183-184: </li></ul><ul><li>12-17; 18-27 </li></ul>