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13-3 Probability.ppt

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smithj91

This document discusses probability and provides examples of calculating probability using dice rolls, game boards with colored sections, and spinners. The key points are: - Probability is the number of successful outcomes divided by the total number of possible outcomes. - For a single die, the probability of rolling a 3 is 1/6 since there is 1 way to roll a 3 out of 6 total possible outcomes. - For two dice, the probability of rolling a 5 is 4/36 since there are 4 ways to roll a 5 (1-4, 2-3, 3-2, 4-1) out of 36 total possible outcomes combining the two dice. - For game boards, probability is calculated by taking the

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JIM SMITH JCHS SPI 3108.5.1
THE PROBABILITY THAT SOMETHING WILL HAPPEN IS THE NUMBER OF SUCCESSFUL OUTCOMES OVER THE TOTAL NUMBER OF OUTCOMES.
LET’S LOOK AT A DIE. IF YOU ROLL ONE DIE, THERE IS ONLY 1 WAY TO GET A 3 SO 1 WILL BE THE NUMBER OF SUCCESSFUL OUTCOMES. YOU CAN ROLL ANY ONE OF 6 NUMBERS SO THERE ARE 6 POSSIBLE OUTCOMES. 6 WILL BE THE TOTAL NUMBER OF OUTCOMES. WITH 1 DIE THE PROBABILITY OF ROLLING A 3 IS 1/6
WHAT IS THE PROBABILITY OF ROLLING A 5? WHAT IS THE PROBABILITY OF ROLLING A 2? WHAT IS THE PROBABILITY OF ROLLING A 7?
LET’S USE 2 DICE. NOW OUR NUMBERS CHANGE. THE TOTAL NUMBER OF POSSIBLE OUTCOMES INCREASES. FOR EVERY NUMBER WE CAN ROLL ON ONE DIE, WE CAN ROLL ONE OF SIX NUMBERS ON THE SECOND DIE.
HERE IS A TABLE DIE 1 DIE 2 1 1,2,3,4,5,6 2 1,2,3,4,5,6 3 1,2,3,4,5,6 4 1,2,3,4,5,6 5 1,2,3,4,5,6 6 1,2,3,4,5,6 36 possibilities
HOW MANY WAYS CAN YOU ROLL A 5? Die 1 Die 2 1 4 2 3 3 2 4 1 4 SUCCESSFUL OUTCOMES
WHAT IS THE PROBABILITY OF ROLLING A 5 WITH 2 DICE? 4/36 or 1/9
PROBABILITY THAT INVOLVES A GEOMETRIC MEASUREMENT SUCH AS LENGTH OR AREA IS CALLED
LET’S LOOK AT GAME BOARDS THE PROBABILITY THAT A DART WILL HIT A CERTAIN COLOR IS…. THE AREA OF THAT COLOR OVER THE AREA OF THE WHOLE BOARD.
IF THE BOARD IS DIVIDED INTO 4 EQUAL PARTS THEN…. THE PROBABILITY OF HITTING GREEN IS 1/4 THE PROBABILITY OF HITTING BLUE IS 2/4 = 1/2 THE PROBABILITY OF HITTING BLACK IS 1/4
FIND THE PROBABILITY OF A DART LANDING IN THE DARK BLUE 10/25 = 2/5 THE LIGHT BLUE 7/25 THE BROWN 3/25 THE GREEN 5/25 = 1/5
6 6 FIND THE PROBABILITY OF A DART LANDING IN THE BLACK AREA
6 6 AREA OF SQUARE – AREA OF CIRCLE OVER AREA OF SQUARE
6 6 AREA OF SQUARE – AREA OF CIRCLE OVER AREA OF SQUARE 36 - 9π 36 (6X6) – (π3²) (6X6) 3 4 4 1 = 4 – π 4
60° FIND THE PROBABILITY OF A SPINNER STOPING ON…. GREEN 90/360 = 1/4 .25 = 25% BLUE 60/360 = 1/6 .17 = 17% YELLOW 210/360 = 7/12 .583 = 58.3%

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13-3 Probability.ppt

  • 2. THE PROBABILITY THAT SOMETHING WILL HAPPEN IS THE NUMBER OF SUCCESSFUL OUTCOMES OVER THE TOTAL NUMBER OF OUTCOMES.
  • 3. LET’S LOOK AT A DIE. IF YOU ROLL ONE DIE, THERE IS ONLY 1 WAY TO GET A 3 SO 1 WILL BE THE NUMBER OF SUCCESSFUL OUTCOMES. YOU CAN ROLL ANY ONE OF 6 NUMBERS SO THERE ARE 6 POSSIBLE OUTCOMES. 6 WILL BE THE TOTAL NUMBER OF OUTCOMES. WITH 1 DIE THE PROBABILITY OF ROLLING A 3 IS 1/6
  • 4. WHAT IS THE PROBABILITY OF ROLLING A 5? WHAT IS THE PROBABILITY OF ROLLING A 2? WHAT IS THE PROBABILITY OF ROLLING A 7?
  • 5. LET’S USE 2 DICE. NOW OUR NUMBERS CHANGE. THE TOTAL NUMBER OF POSSIBLE OUTCOMES INCREASES. FOR EVERY NUMBER WE CAN ROLL ON ONE DIE, WE CAN ROLL ONE OF SIX NUMBERS ON THE SECOND DIE.
  • 6. HERE IS A TABLE DIE 1 DIE 2 1 1,2,3,4,5,6 2 1,2,3,4,5,6 3 1,2,3,4,5,6 4 1,2,3,4,5,6 5 1,2,3,4,5,6 6 1,2,3,4,5,6 36 possibilities
  • 7. HOW MANY WAYS CAN YOU ROLL A 5? Die 1 Die 2 1 4 2 3 3 2 4 1 4 SUCCESSFUL OUTCOMES
  • 8. WHAT IS THE PROBABILITY OF ROLLING A 5 WITH 2 DICE? 4/36 or 1/9
  • 9. PROBABILITY THAT INVOLVES A GEOMETRIC MEASUREMENT SUCH AS LENGTH OR AREA IS CALLED
  • 10. LET’S LOOK AT GAME BOARDS THE PROBABILITY THAT A DART WILL HIT A CERTAIN COLOR IS…. THE AREA OF THAT COLOR OVER THE AREA OF THE WHOLE BOARD.
  • 11. IF THE BOARD IS DIVIDED INTO 4 EQUAL PARTS THEN…. THE PROBABILITY OF HITTING GREEN IS 1/4 THE PROBABILITY OF HITTING BLUE IS 2/4 = 1/2 THE PROBABILITY OF HITTING BLACK IS 1/4
  • 12. FIND THE PROBABILITY OF A DART LANDING IN THE DARK BLUE 10/25 = 2/5 THE LIGHT BLUE 7/25 THE BROWN 3/25 THE GREEN 5/25 = 1/5
  • 13. 6 6 FIND THE PROBABILITY OF A DART LANDING IN THE BLACK AREA
  • 14. 6 6 AREA OF SQUARE – AREA OF CIRCLE OVER AREA OF SQUARE
  • 15. 6 6 AREA OF SQUARE – AREA OF CIRCLE OVER AREA OF SQUARE 36 - 9Ï€ 36 (6X6) – (Ï€3²) (6X6) 3 4 4 1 = 4 – Ï€ 4
  • 16. 60° FIND THE PROBABILITY OF A SPINNER STOPING ON…. GREEN 90/360 = 1/4 .25 = 25% BLUE 60/360 = 1/6 .17 = 17% YELLOW 210/360 = 7/12 .583 = 58.3%