IXL - Sample spaces for compound events (Geometry practice)

Celine spins this spinner two times.

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

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question

Liam flips this coin 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:

flipping a coin and
flipping the coin again.

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

The first row of the tree diagram will represent flipping the coin the first time. The coin has 2 sides: 1 with heads (H) and 1 with tails (T). So, the first row of the tree diagram will have 2 branches.

The second row of the tree diagram will represent flipping the coin the second time. So, each branch will have 2 more branches.

Notice there are 4 branches on the bottom row of the tree diagram. Each of these branches represents 1 of the 4 equally likely outcomes in the sample space:

landing on heads twice
landing on heads then tails
landing on tails then heads
landing on tails twice

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II.1Sample spaces of simple events

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