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Probability

Probability. Independent and Dependent Events. Y. Y. Y. R. R. R. B. B. B. Independent Events. Independent Events – the first event does not affect the second event

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Probability

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  1. Probability Independent and Dependent Events

  2. Y Y Y R R R B B B Independent Events • Independent Events – the first event does not affect the second event • Example – Draw a cube from a bag that contains one yellow, one red, and one blue cube. Replace the cube and draw another cube. Outcomes Event 1 Event 2 Y,Y Y,R Y,B R,Y R,R R,B B,Y B,R B,B Y R B

  3. Y Y Y R R R B B B Independent Events • Independent Events – the first event does not affect the second event • Example – Draw a cube from a bag that contains one yellow, one red, and one blue cube. Replace the cube and draw another cube. Outcomes Event 1 Event 2 Y,Y Y,R Y,B R,Y R,R R,B B,Y B,R B,B Y R B

  4. Y Y Y R R R B B B Independent Events • Independent Events – the first event does not affect the second event • Example – Draw a cube from a bag that contains one yellow, one red, and one blue cube. Replace the cube and draw another cube. Outcomes Event 1 Event 2 Y,Y Y,R Y,B R,Y R,R R,B B,Y B,R B,B Y R B

  5. Y Y Y R R R B B B Independent Events • Independent Events – the first event does not affect the second event • Example – Draw a cube from a bag that contains one yellow, one red, and one blue cube. Replace the cube and draw another cube. Outcomes Event 1 Event 2 Y,Y Y,R Y,B R,Y R,R R,B B,Y B,R B,B Y R B

  6. Y Y Y R R R B B B Independent Events • Independent Events – the first event does not affect the second event • Example – Draw a cube from a bag that contains one yellow, one red, and one blue cube. Replace the cube and draw another cube. Outcomes Event 1 Event 2 Y,Y Y,R Y,B R,Y R,R R,B B,Y B,R B,B Y R B

  7. Y Y Y R R R B B B Independent Events • Independent Events – the first event does not affect the second event • Example – Draw a cube from a bag that contains one yellow, one red, and one blue cube. Replace the cube and draw another cube. Outcomes Event 1 Event 2 Y,Y Y,R Y,B R,Y R,R R,B B,Y B,R B,B Y R B

  8. Y Y Y R R R B B B Independent Events • Independent Events – the first event does not affect the second event • Example – Draw a cube from a bag that contains one yellow, one red, and one blue cube. Replace the cube and draw another cube. Outcomes Event 1 Event 2 Y,Y Y,R Y,B R,Y R,R R,B B,Y B,R B,B Y R B

  9. Dependent Events • Dependent Events – the first event does affect the second event • Example – Draw a cube from a bag that contains one yellow, one red, and one blue cube. Don’t replace the cube and draw another cube. Outcomes Event 1 Event 2 Y,R Y,B R,Y R,B B,Y B,R R Y B Y R B Y B R

  10. Dependent Events • Dependent Events – the first event does affect the second event • Example – Draw a cube from a bag that contains one yellow, one red, and one blue cube. Don’t replace the cube and draw another cube. Outcomes Event 1 Event 2 Y,R Y,B R,Y R,B B,Y B,R R Y B Y R B Y B R

  11. Dependent Events • Dependent Events – the first event does affect the second event • Example – Draw a cube from a bag that contains one yellow, one red, and one blue cube. Don’t replace the cube and draw another cube. Outcomes Event 1 Event 2 Y,R Y,B R,Y R,B B,Y B,R R Y B Y R B Y B R

  12. Dependent Events • Dependent Events – the first event does affect the second event • Example – Draw a cube from a bag that contains one yellow, one red, and one blue cube. Don’t replace the cube and draw another cube. Outcomes Event 1 Event 2 Y,R Y,B R,Y R,B B,Y B,R R Y B Y R B Y B R

  13. Dependent Events • Dependent Events – the first event does affect the second event • Example – Draw a cube from a bag that contains one yellow, one red, and one blue cube. Don’t replace the cube and draw another cube. Outcomes Event 1 Event 2 Y,R Y,B R,Y R,B B,Y B,R R Y B Y R B Y B R

  14. Dependent Events • Dependent Events – the first event does affect the second event • Example – Draw a cube from a bag that contains one yellow, one red, and one blue cube. Don’t replace the cube and draw another cube. Outcomes Event 1 Event 2 Y,R Y,B R,Y R,B B,Y B,R R Y B Y R B Y B R

  15. Dependent Events • Dependent Events – the first event does affect the second event • Example – Draw a cube from a bag that contains one yellow, one red, and one blue cube. Don’t replace the cube and draw another cube. Outcomes Event 1 Event 2 Y,R Y,B R,Y R,B B,Y B,R R Y B Y R B Y B R

  16. Y Y Y R R R B B B Independent Events • To determine the probability of independent events, you can use multiplication: multiply P(E1) x P(E2) n = the number of favorable outcomes n n n − x − = − 3 3 9 Outcomes Event 1 Event 2 Y,Y Y,R Y,B R,Y R,R R,B B,Y B,R B,B Y R B

  17. Dependent Events • To determine the probability of dependent events, you can use multiplication: multiply P(E1) x P(E2) n = the number of favorable outcomes n n n − x − = − 3 2 6 Outcomes Event 1 Event 2 Y,R Y,B R,Y R,B B,Y B,R R Y B Y R B Y B R

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