IXL | Samples spaces for compound events using tables

Sofia spins each of these spinners once.

Which table represents the sample space of this compound event?

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Learn with an example

question

Emma picks one marble from a bag. Then, she puts the marble back in the bag and picks a marble again. The bag has 1 blue marble, 1 green marble, and 1 yellow marble.

Which table 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 a compound event with a table. Each cell of the table represents one outcome.

solution

This compound event is made of two simple events:

picking a marble and
picking a marble again.

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

The rows will represent the marble Emma picks the first time. Make a row for each marble. There is 1 blue marble, 1 green marble, and 1 yellow marble.

The columns will represent the marble Emma picks the second time. Make a column for each marble.

	blue (B)	green (G)	yellow (Y)
blue (B)
green (G)
yellow (Y)

Now, write the combinations formed by the intersecting rows and columns.

	blue (B)	green (G)	yellow (Y)
blue (B)	BB	BG	BY
green (G)	GB	GG	GY
yellow (Y)	YB	YG	YY

Notice there are 9 cells in the table. Each cell represents 1 of the 9 equally likely outcomes in the sample space:

picking the blue marble twice
picking the blue marble then the green marble
picking the blue marble then the yellow marble
picking the green marble then the blue marble
picking the green marble twice
picking the green marble then the yellow marble
picking the yellow marble then the blue marble
picking the yellow marble then the green marble
picking the yellow marble twice

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Work it out

Not feeling ready yet? This can help:

II.1Sample spaces of simple events

	orange (O)	purple (P)	green (G)
red (R)	RO	RP	RG
blue (B)	BO	BP	BG
yellow (Y)	YO	YP	YG

	orange (O)	purple (P)	green (G)
red (R)	RO	RP	RG
yellow (Y)	YO	YP	YG

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