IXL | Sample spaces for compound events using lists and tables

Sasha chooses one of these cards from a deck. Then, she puts the card back in the deck and chooses a card again.

Which table represents the sample space of this compound event?

	1	7	5	7	9
1	1, 1	1, 7	1, 5	1, 7	1, 9
3	3, 1	3, 7	3, 5	3, 7	3, 9
5	5, 1	5, 7	5, 5	5, 7	5, 9
7	7, 1	7, 7	7, 5	7, 7	7, 9
9	9, 1	9, 7	9, 5	9, 7	9, 9

	1	3	5	7	9
1	1, 1	1, 3	1, 5	1, 7	1, 9
3	3, 1	3, 3	3, 5	3, 7	3, 9
5	5, 1	5, 3	5, 5	5, 7	5, 9
7	7, 1	7, 3	7, 5	7, 7	7, 9
9	9, 1	9, 3	9, 5	9, 7	9, 9

ref_doc_title.

Learn with an example

question

Jason flips this coin once and spins this spinner once.

A penny and a spinner with 7 equal sections. The sections are labeled: 0, 1, 2, 3, 4, 5, and 6.

Which table represents the sample space of this compound event?

	0	1	2	3	4
heads (H)	H, 0	H, 1	H, 2	H, 3	H, 4
tails (T)	T, 0	T, 1	T, 2	T, 3	T, 4

	0	1	2	3	4	5	6
heads (H)	H, 0	H, 1	H, 2	H, 3	H, 4	H, 5	H, 6
tails (T)	T, 0	T, 1	T, 2	T, 3	T, 4	T, 5	T, 6

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:

flipping a coin and
spinning a spinner.

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

Make a row for each side of the coin. There is 1 side with heads and 1 side with tails.

Make a column for each section of the spinner. There is 1 section labeled 0, 1 section labeled 1, 1 section labeled 2, 1 section labeled 3, 1 section labeled 4, 1 section labeled 5, and 1 section labeled 6.

	0	1	2	3	4	5	6
heads (H)
tails (T)

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

	0	1	2	3	4	5	6
heads (H)	H, 0	H, 1	H, 2	H, 3	H, 4	H, 5	H, 6
tails (T)	T, 0	T, 1	T, 2	T, 3	T, 4	T, 5	T, 6

Notice there are 14 cells in the table. Each cell represents 1 of the 14 equally likely outcomes in the sample space:

landing on heads and spinning a 0
landing on heads and spinning a 1
landing on heads and spinning a 2
landing on heads and spinning a 3
landing on heads and spinning a 4
landing on heads and spinning a 5
landing on heads and spinning a 6
landing on tails and spinning a 0
landing on tails and spinning a 1
landing on tails and spinning a 2
landing on tails and spinning a 3
landing on tails and spinning a 4
landing on tails and spinning a 5
landing on tails and spinning a 6

$Confetti$

Excellent!

Now entering the Challenge Zone—are you ready?

Questions
answeredQuestions

Time
elapsedTime

hr	min	sec
00	00	04

SmartScore
out of 100
IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100)! Learn more

Teacher tools

Work it out

Not feeling ready yet? This can help:

II.1Sample spaces of simple events

Excellent! You got that right!

Jumping to level 1 of 1

Excellent!