IXL - Find probabilities using two-way frequency tables (Algebra 1 practice)

A dentist was making note of his upcoming appointments with different aged patients and the reasons for their visits.

	Patients under 18	Patients 19-60
Regular cleaning	6	2
Broken tooth	3	4

What is the probability that a randomly selected appointment is for a regular cleaning and is with a patient under 18?

Simplify any fractions.

ref_doc_title.

Learn with an example

question

On a reality show, contestants had to spin two wheels of fate. Spinning the first wheel determined the remote location where contestants would reside for the duration of the season. Spinning the second wheel determined which "bonus survival tool" they would be allowed to bring, along with a few other necessary items.

	A tent	Matches
Desert	1	5
Rainforest	2	4

What is the probability that a randomly selected participant spun the first wheel and landed on rainforest and spun the second wheel and landed on a tent?

Simplify any fractions.

key idea

A uniform probability model is a sample space in which all outcomes are equally likely.

In a uniform probability model, the probability of an event

is the number of outcomes in that event divided by the total number of outcomes in the sample space:

(

)

# of outcomes in C

total # of outcomes

solution

Let

be the event "the participant spun the first wheel and landed on rainforest" and

be the event "the participant spun the second wheel and landed on a tent".

To find the probability that a participant spun the first wheel and landed on rainforest and spun the second wheel and landed on a tent, first identify the sample space and the event.

The outcomes in the sample space are the different participants. Each participant is equally likely to be selected, so this is a uniform probability model.

The event is

and

"the participant spun the first wheel and landed on rainforest and spun the second wheel and landed on a tent".

Since this is a uniform probability model, count the number of outcomes in the event

and

and count the total number of outcomes. Then, divide them to compute the probability.

Find the number of outcomes in the event

and

is the event "the participant spun the first wheel and landed on rainforest and spun the second wheel and landed on a tent", so look at the table to see how many participants spun the first wheel and landed on rainforest and spun the second wheel and landed on a tent.

	A tent	Matches
Desert	1	5
Rainforest	2	4

The number of participants who spun the first wheel and landed on rainforest and spun the second wheel and landed on a tent is 2.

Find the total number of outcomes.

Add all the numbers in the table to find the total number of participants.

	A tent	Matches
Desert	1	5
Rainforest	2	4

Find

(

A and B

)

Since all outcomes are equally likely, the probability of event

and

is the number of outcomes in event

and

divided by the total number of outcomes.

(

A and B

)

# of outcomes in A and B

total # of outcomes

The probability that a participant spun the first wheel and landed on rainforest and spun the second wheel and landed on a tent is

Looking for more? Try these:

Lesson: Two-way tables

$Confetti$

Excellent!

Now entering the Challenge Zone—are you ready?

Questions
answeredQuestions

Time
elapsedTime

hr	min	sec
00	00	06

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? These can help:

JJ.4Find probabilities using two-way frequency tables

KK.1Theoretical probability

Lesson: Two-way tables

Excellent! You got that right!

Jumping to level 1 of 1

Excellent!