IXL | Sample spaces for compound events using lists and tables

Kate spins this spinner twice.

Which table represents the sample space of this compound event?

	blue (B)	green (G)	yellow (Y)	red (R)	purple (P)
blue (B)	BB	BG	BY	BR	BP
green (G)	GB	GG	GY	GR	GP
yellow (Y)	YB	YG	YY	YR	YP
red (R)	RB	RG	RY	RR	RP
purple (P)	PB	PG	PY	PR	PP

	blue (B)	green (G)	blue (B)	red (R)	purple (P)
blue (B)	BB	BG	BB	BR	BP
green (G)	GB	GG	GB	GR	GP
yellow (Y)	YB	YG	YB	YR	YP
red (R)	RB	RG	RB	RR	RP
purple (P)	PB	PG	PB	PR	PP

ref_doc_title.

Learn with an example

question

Samir picks one of these tiles from a bag. Then, he puts the tile back in the bag and picks a tile again.

Which table represents the sample space of this compound event?

	A	E	I	O	U
A	AA	AE	AI	AO	AU
E	EA	EE	EI	EO	EU
I	IA	IE	II	IO	IU
O	OA	OE	OI	OO	OU
U	UA	UE	UI	UO	UU

	A	E	I	O	U
A	AA	AE	AI	AO	AU
E	EA	EE	EI	EO	EU
O	OA	OE	OI	OO	OU
O	OA	OE	OI	OO	OU
U	UA	UE	UI	UO	UU

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:

choosing a tile and
choosing a tile again.

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

The rows will represent the first tile. Make a row for each tile. There is 1 tile labeled A, 1 tile labeled E, 1 tile labeled I, 1 tile labeled O, and 1 tile labeled U.

The columns will represent the second tile. Make a column for each tile.

	A	E	I	O	U
A
E
I
O
U

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

	A	E	I	O	U
A	AA	AE	AI	AO	AU
E	EA	EE	EI	EO	EU
I	IA	IE	II	IO	IU
O	OA	OE	OI	OO	OU
U	UA	UE	UI	UO	UU

Notice there are 25 cells in the table. Each cell represents 1 of the 25 equally likely outcomes in the sample space:

choosing the A tile twice
choosing the A tile then the E tile
choosing the A tile then the I tile
choosing the A tile then the O tile
choosing the A tile then the U tile
choosing the E tile then the A tile
choosing the E tile twice
choosing the E tile then the I tile
choosing the E tile then the O tile
choosing the E tile then the U tile
choosing the I tile then the A tile
choosing the I tile then the E tile
choosing the I tile twice
choosing the I tile then the O tile
choosing the I tile then the U tile
choosing the O tile then the A tile
choosing the O tile then the E tile
choosing the O tile then the I tile
choosing the O tile twice
choosing the O tile then the U tile
choosing the U tile then the A tile
choosing the U tile then the E tile
choosing the U tile then the I tile
choosing the U tile then the O tile
choosing the U tile twice

$Confetti$

Excellent!

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II.1Sample spaces of simple events

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