Transcript Compound Events

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
Lizzy
Amber
Isaiah
Lizzy
Amber
Georgie
Lizzy
Amber
Jenna
Lizzy
Amber
Chart
Lizzy
Amber
Demetrius
Demetrius, Lizzy
Demetrius, Amber
Isaiah
Isaiah, Lizzy
Isaiah, Amber
Georgie
Georgie, Lizzy
Georgie, Amber
Jenna
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.
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mxn
4 president candidates x 2 vp candidates
8 pres/vp outcomes
Examples
How many outcomes?
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Toss a penny and roll a 6 sides die
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.
Put together and outfit from a selection of 4
shirts, 2 pairs of pants, and 2 sweaters.
Definitions
Independent event
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Events that do not effect on each other
Pick a marble, put it back, then pick another
marble
P(A,B) = P(A) x P(B)
Dependent event
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Events that do effect each other
Pick a marble, keep it, then pick another
marble
P(A,B) = P(A) x P(B after A)
Examples
A bag contains 10 cubes: 5 red, 3 blue,
and 2 green.
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P(R, G)
P(G, R)
P(G, B)
P(R, G or B)