Compound Events SWBAT use tree diagrams and tables to find possible outcomes; find the number of possible outcomes using the counting principle; find the.

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Presentation transcript:

Compound Events SWBAT use tree diagrams and tables to find possible outcomes; find the number of possible outcomes using the counting principle; find the probability of independent and dependent compound events

How could we solve this? Demetrius, Isaiah, Georgie, and Jenna are all running to be president of their class. Lizzy and Amber are both running for vice president. How many different combinations of president and vice president could we have?

Tree Diagrams Draw a tree diagram to illustrate the various ways the event can occur. Demetrius Isaiah Georgie Jenna Lizzy Amber Lizzy Amber Lizzy Amber Lizzy Amber

Chart LizzyAmber Demetrius Isaiah Georgie Jenna Demetrius, Lizzy Demetrius, Amber Isaiah, Lizzy Isaiah, Amber Georgie, LizzyGeorgie, Amber Jenna, Lizzy Jenna, Amber

Counting Principle If one evens has m possible outcomes and second event has n possible outcomes, then there are m x n possible outcomes for the two events together. m x n m x n 4 president candidates x 2 vp candidates 4 president candidates x 2 vp candidates 8 pres/vp outcomes 8 pres/vp outcomes

Examples How many outcomes? Toss a penny and roll a 6 sides die Toss a penny and roll a 6 sides die Spin a 4 number spinner and choose a marble from a bag of 3. Spin a 4 number spinner and choose a marble from a bag of 3. Make a sandwich with 5 different types of bread and 2 different fillings. Make a sandwich with 5 different types of bread and 2 different fillings. Put together and outfit from a selection of 4 shirts, 2 pairs of pants, and 2 sweaters. Put together and outfit from a selection of 4 shirts, 2 pairs of pants, and 2 sweaters.

Definitions Independent event Events that do not effect on each other Events that do not effect on each other Pick a marble, put it back, then pick another marble Pick a marble, put it back, then pick another marble P(A,B) = P(A) x P(B) P(A,B) = P(A) x P(B) Dependent event Events that do effect each other Events that do effect each other Pick a marble, keep it, then pick another marble Pick a marble, keep it, then pick another marble P(A,B) = P(A) x P(B after A) P(A,B) = P(A) x P(B after A)

Examples A bag contains 10 cubes: 5 red, 3 blue, and 2 green. P(R, G) P(R, G) P(G, R) P(G, R) P(G, B) P(G, B) P(R, G or B) P(R, G or B)