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

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

	Caffeine-free	Caffeinated
Mint	3	4
Fruity	4	2

What is the probability that a randomly selected tea is caffeine-free given that the tea is mint?

Simplify any fractions.

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Learn with an example

question

Nick likes to go on canoe trips, and on each trip he purchases oars to keep as souvenirs. His collection of oars is organized by decade and type of wood.

	Spruce wood	Ash wood
2010s	6	9
2020s	2	2

What is the probability that a randomly selected oar was made from ash wood given that the oar was purchased in the 2020s?

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 conditional probability an event

occurs given that an event

occurs is written

(

It is the number of outcomes in

and

divided by the number of outcomes in

(

A|B

)

# of outcomes in A and B

total # of outcomes in B

solution

Let

be the event "the oar was made from ash wood" and

be the event "the oar was purchased in the 2020s".

To find the probability that a randomly selected oar was made from ash wood given that the oar was purchased in the 2020s, first identify the sample space.

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

The probability that a randomly selected oar was made from ash wood given that the oar was purchased in the 2020s can be expressed as

(

A|B

)

Since this is a uniform probability model,

(

A|B

)

# of outcomes in A and B

# of outcomes in B

Find the number of outcomes in the event

and

is the event "the oar was made from ash wood and was purchased in the 2020s". Look at the table to see how many oars were made from ash wood and were purchased in the 2020s.

	Spruce wood	Ash wood
2010s	6	9
2020s	2	2

The number of oars that were made from ash wood and were purchased in the 2020s is 2.

Find the number of outcomes in the event

is the event "the oar was purchased in the 2020s", so look at the table to see how many oars were purchased in the 2020s.

	Spruce wood	Ash wood
2010s	6	9
2020s	2	2

The number of oars that were purchased in the 2020s is

Find

(

A|B

)

To find the probability that

occurs given that

occurs, use the formula for conditional probability in a uniform probability model.

(

A|B

)

# of outcomes in A and B

# of outcomes in B

The probability that a randomly selected oar was made from ash wood given that the oar was purchased in the 2020s is

Looking for more? Try these:

Lesson: Conditional probability

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Work it out

Not feeling ready yet? These can help:

CC.4Find probabilities using two-way frequency tables

CC.6Find conditional probabilities

Lesson: Conditional probability

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