IXL - Sample spaces for compound events (Algebra 2 practice)

Lee spins this spinner once and rolls this die one time.

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

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question

Joseph chooses one of these cards from a deck. Then he puts the card back in the deck and chooses a card again.

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:

choosing a card and
choosing a card again.

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

The first row of the tree diagram will represent choosing the first card. The deck has 3 cards: 1 with 7, 1 with 8, and 1 with 9. So, the first row of the tree diagram will have 3 branches.

The second row of the tree diagram will represent choosing the second card. 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:

choosing the 7 card twice
choosing the 7 card then the 8 card
choosing the 7 card then the 9 card
choosing the 8 card then the 7 card
choosing the 8 card twice
choosing the 8 card then the 9 card
choosing the 9 card then the 7 card
choosing the 9 card then the 8 card
choosing the 9 card twice

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II.1Sample spaces of simple events

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