IXL | Sample spaces for compound events

Donald picks one marble from a bag. Then he puts the marble back in the bag and picks a marble again. The bag has 1 red marble, 1 blue marble, and 1 green marble.

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

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question

Marshall picks one of these tiles and flips this coin one time.

Five tiles and a dime. There is one letter on each tile. The letters are "A," B, C, D, and "E."

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:

picking a tile and
flipping a coin.

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

There are 5 tiles: 1 with an A, 1 with a B, 1 with a C, 1 with a D, and 1 with an E. So, the first row of the tree diagram will have 5 branches.

The coin has 2 sides: 1 with heads (H) and 1 with tails (T). So, each branch will have 2 more branches.

Notice there are 10 branches on the bottom row of the tree diagram. Each of these branches represents 1 of the 10 equally likely outcomes in the sample space:

picking the A tile and flipping heads
picking the A tile and flipping tails
picking the B tile and flipping heads
picking the B tile and flipping tails
picking the C tile and flipping heads
picking the C tile and flipping tails
picking the D tile and flipping heads
picking the D tile and flipping tails
picking the E tile and flipping heads
picking the E tile and flipping tails

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II.1Sample spaces of simple events

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