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

A wilderness retail store asked a consulting company to do an analysis of their hiking shoe customers. The consulting company gathered data from each customer who purchased hiking shoes, and recorded the shoe brand and the customer's level of happiness.

	Displeased	Pleased
A Footlong shoe	4	4
A Toes Knows shoe	6	4

What is the probability that a randomly selected customer purchased a Footlong shoe and is pleased?

Simplify any fractions.

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Learn with an example

question

A college professor asked his psychology students to complete a personality test. He paid special attention to his students' career goals and their greatest fears.

	Social worker	Therapist
Fear of snakes	4	5
Fear of heights	2	3

What is the probability that a randomly selected student has a fear of heights and wants to be a therapist?

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 student has a fear of heights" and

be the event "the student wants to be a therapist".

To find the probability that a student has a fear of heights and wants to be a therapist, first identify the sample space and the event.

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

The event is

and

"the student has a fear of heights and wants to be a therapist".

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 student has a fear of heights and wants to be a therapist", so look at the table to see how many students have a fear of heights and want to be a therapist.

	Social worker	Therapist
Fear of snakes	4	5
Fear of heights	2	3

The number of students who have a fear of heights and want to be a therapist is 3.

Find the total number of outcomes.

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

	Social worker	Therapist
Fear of snakes	4	5
Fear of heights	2	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 student has a fear of heights and wants to be a therapist 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:

CC.1Calculate probabilities of events

JJ.1Probability of simple events

Lesson: Two-way tables

Lesson: Probability

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