IXL | Find probabilities using two-way frequency tables

Reba attended her town's annual Worm Charming Competition. Contestants are assigned to a square foot of land, where they have 30 minutes to "charm" worms to the surface of the dirt using a single technique. Reba observed contestants' charming techniques, and kept track of how many worms surfaced.

	Tapping the ground	Raking the ground
5-10 worms	3	5
11-20 worms	2	3

What is the probability that a randomly selected contestant charmed 5-10 worms and tried tapping the ground?

Simplify any fractions.

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Learn with an example

question

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.

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 appointment is for a regular cleaning" and

be the event "the appointment is with a patient under 18".

To find the probability that an appointment is for a regular cleaning and is with a patient under 18, first identify the sample space and the event.

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

The event is

and

"the appointment is for a regular cleaning and is with a patient under 18".

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 appointment is for a regular cleaning and is with a patient under 18", so look at the table to see how many appointments are for a regular cleaning and are with patients under 18.

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

The number of appointments that are for a regular cleaning and are with patients under 18 is 6.

Find the total number of outcomes.

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

	Patients under 18	Patients 19-60
Regular cleaning	6	2
Broken tooth	3	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 an appointment is for a regular cleaning and is with a patient under 18 is

Looking for more? Try these:

Lesson: Two-way tables

Lesson: Probability

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II.2Probability of simple events

Lesson: Two-way tables

Lesson: Probability

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