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

Antonio designs bow ties for a local boutique store. The store manager counted the ties currently on display, tracking them by material and shape.

	Butterfly	Batwing
Cotton	1	4
Suede	4	6

What is the probability that a randomly selected bow tie is made of suede given that the bow tie is shaped like a butterfly?

Simplify any fractions.

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question

Antonio designs bow ties for a local boutique store. The store manager counted the ties currently on display, tracking them by material and shape.

	Butterfly	Batwing
Cotton	1	4
Suede	4	6

What is the probability that a randomly selected bow tie is made of suede given that the bow tie is shaped like a butterfly?

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 bow tie is made of suede" and

be the event "the bow tie is shaped like a butterfly".

To find the probability that a randomly selected bow tie is made of suede given that the bow tie is shaped like a butterfly, first identify the sample space.

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

The probability that a randomly selected bow tie is made of suede given that the bow tie is shaped like a butterfly 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 bow tie is made of suede and is shaped like a butterfly". Look at the table to see how many bow ties are made of suede and are shaped like a butterfly.

	Butterfly	Batwing
Cotton	1	4
Suede	4	6

The number of bow ties that are made of suede and are shaped like a butterfly is 4.

Find the number of outcomes in the event

is the event "the bow tie is shaped like a butterfly", so look at the table to see how many bow ties are shaped like a butterfly.

	Butterfly	Batwing
Cotton	1	4
Suede	4	6

The number of bow ties that are shaped like a butterfly 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 bow tie is made of suede given that the bow tie is shaped like a butterfly is

Looking for more? Try these:

Lesson: Conditional probability

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Not feeling ready yet? These can help:

AA.9Find probabilities using two-way frequency tables

AA.11Find conditional probabilities

Lesson: Conditional probability

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