IXL | Find probabilities using two-way frequency tables

After growing tired of squinting while driving, Will went shopping for a pair of sunglasses. He tried on glasses with different frames and lenses.

	Cat eye frames	Browline frames
Polarized lenses	3	4
Regular lenses	3	4

What is the probability that a randomly selected pair of sunglasses has regular lenses and browline frames?

Simplify any fractions.

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Learn with an example

question

Mike, a soup chef at a new restaurant, kept track of the first day's soup sales.

	Cup	Bowl
Split pea	6	6
Chicken noodle	3	3

What is the probability that a randomly selected soup was chicken noodle and was ordered in a bowl?

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 soup was chicken noodle" and

be the event "the soup was ordered in a bowl".

To find the probability that a soup was chicken noodle and was ordered in a bowl, first identify the sample space and the event.

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

The event is

and

"the soup was chicken noodle and was ordered in a bowl".

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 soup was chicken noodle and was ordered in a bowl", so look at the table to see how many soups were chicken noodle and were ordered in a bowl.

	Cup	Bowl
Split pea	6	6
Chicken noodle	3	3

The number of soups that were chicken noodle and were ordered in a bowl is 3.

Find the total number of outcomes.

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

	Cup	Bowl
Split pea	6	6
Chicken noodle	3	3

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 soup was chicken noodle and was ordered in a bowl is

Looking for more? Try these:

Lesson: Two-way tables

Lesson: Probability

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Teacher tools

Work it out

Not feeling ready yet? These can help:

JJ.1Probability of simple events

JJ.3Experimental probability

Lesson: Two-way tables

Lesson: Probability

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