IXL | Find probabilities using two-way frequency tables

Chef Henderson baked her famous casseroles for a company holiday party. The casseroles have different shapes and different delicious fillings.

	Spinach	Cheese
Rectangle	2	4
Circle	4	4

What is the probability that a randomly selected casserole is shaped like a circle and is filled with cheese?

Simplify any fractions.

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Learn with an example

question

Victoria is a pediatrics nurse who conducts the first neonatal exam on newborn patients. She makes note of the newborns' height, weight, eye color, and heart rate, among other things.

	Brown eyes	Blue eyes
Slow heart rate ( <100 bpm)	3	2
Fast heart rate ( >100 bpm)	6	4

What is the probability that a randomly selected baby has a slow heart rate

(

<100

bpm) and has blue eyes?

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 baby has a slow heart rate

(

<100

bpm)" and

be the event "the baby has blue eyes".

To find the probability that a baby has a slow heart rate

(

<100

bpm) and has blue eyes, first identify the sample space and the event.

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

The event is

and

"the baby has a slow heart rate

(

<100

bpm) and has blue eyes".

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 baby has a slow heart rate

(

<100

bpm) and has blue eyes", so look at the table to see how many babies have a slow heart rate

(

<100

bpm) and have blue eyes.

	Brown eyes	Blue eyes
Slow heart rate ( <100 bpm)	3	2
Fast heart rate ( >100 bpm)	6	4

The number of babies who have a slow heart rate

(

<100

bpm) and have blue eyes is 2.

Find the total number of outcomes.

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

	Brown eyes	Blue eyes
Slow heart rate ( <100 bpm)	3	2
Fast heart rate ( >100 bpm)	6	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 baby has a slow heart rate

(

<100

bpm) and has blue eyes is

Looking for more? Try these:

Lesson: Two-way tables

Lesson: Probability

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Teacher tools

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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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