IXL - Find probabilities using two-way frequency tables (Algebra 2 practice)

Clayton works at a coffee shop on weekends. Every now and then, a customer will order a hot tea and ask Clayton to surprise them with the flavor. The teas are categorized by flavor and caffeine level.

	Mint	Fruity
Caffeine-free	4	3
Caffeinated	6	3

What is the probability that a randomly selected tea is caffeine-free and fruity?

Simplify any fractions.

ref_doc_title.

Learn with an example

question

Tim joined a book club to spend more quality time with his cousin. At the first meeting, club members recorded how many hours a week they typically read and whether they preferred e-readers or paperback books.

	E-readers	Paperback books
About 1 hour per week	6	3
About 3 hours per week	2	6

What is the probability that a randomly selected club member reads about 1 hour per week and prefers paperback books?

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 club member reads about 1 hour per week" and

be the event "the club member prefers paperback books".

To find the probability that a club member reads about 1 hour per week and prefers paperback books, first identify the sample space and the event.

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

The event is

and

"the club member reads about 1 hour per week and prefers paperback books".

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 club member reads about 1 hour per week and prefers paperback books", so look at the table to see how many club members read about 1 hour per week and prefer paperback books.

	E-readers	Paperback books
About 1 hour per week	6	3
About 3 hours per week	2	6

The number of club members who read about 1 hour per week and prefer paperback books is 3.

Find the total number of outcomes.

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

	E-readers	Paperback books
About 1 hour per week	6	3
About 3 hours per week	2	6

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 club member reads about 1 hour per week and prefers paperback books 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:

OO.1Calculate probabilities of events

JJ.1Probability of simple events

KK.3Find probabilities using two-way frequency tables

Lesson: Two-way tables

Lesson: Probability

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