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Compound events: find the number of outcomes

A compound event consists of two or more simple events. A tree diagram may be useful in identifying the set of all possible outcomes for a compound event.

Consider a probability experiment that consists of two activities: tossing a fair coin and rolling a six-sided cube in which each side of the cube is labeled with a different number from 1 to 6. Each possible outcome represents a compound event.

Make a tree diagram, then count the branches.

The first event has 2 outcomes: heads (H) and tails (T)

The second event has 6 outcomes: 1,2,3,4,5, and 6.

The set of possible outcomes can be described as a set of 12 ordered pairs:

 sample space = { (H,1),(H,2),(H,3),(H,4),(H,5),(H,6) (T,1),(T,2),(T,3),(T,4),(T,5),(T,6) }