IXL | Samples spaces for compound events using tree diagrams

Cooper flips this coin two times.

Which tree diagram represents the sample space of this compound event?

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question

Tessa spins this spinner two times.

Which tree diagram represents the sample space of this compound event?

key idea

The sample space of an event is the set of all possible outcomes of the event.

A compound event is made up of two or more simple events.

You can represent the sample space of an event with a tree diagram. Make one branch for each outcome.

solution

This compound event is made of two simple events:

spinning a spinner and
spinning the spinner again.

You can represent the sample space of the compound event with a tree diagram.

The first row of the tree diagram will represent spinning the spinner the first time. The spinner has 3 sections: 1 with purple (P), 1 with green (G), and 1 with orange (O). So, the first row of the tree diagram will have 3 branches.

The second row of the tree diagram will represent spinning the spinner the second time. So, each branch will have 3 more branches.

Notice there are 9 branches on the bottom row of the tree diagram. Each of these branches represents 1 of the 9 equally likely outcomes in the sample space:

landing on purple twice
landing on purple then green
landing on purple then orange
landing on green then purple
landing on green twice
landing on green then orange
landing on orange then purple
landing on orange then green
landing on orange twice

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II.1Sample spaces of simple events

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