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

On the first day of music class, students submitted a survey. One survey question asked students to report which music genre they prefer. Another question asked students how frequently they sing in the shower.

	0 times a week	1-2 times a week
Country	4	5
Rock	5	4

What is the probability that a randomly selected student prefers country given that the student sings in the shower 1-2 times a week?

Simplify any fractions.

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Learn with an example

question

Liz and her brother are at a store shopping for a beanbag chair for their school's library. The store sells beanbag chairs with different fabrics and types of filling.

	Foam	Beads
Velvet	4	5
Suede	3	4

What is the probability that a randomly selected beanbag chair is made from suede given that the beanbag chair is filled with beads?

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 beanbag chair is made from suede" and

be the event "the beanbag chair is filled with beads".

To find the probability that a randomly selected beanbag chair is made from suede given that the beanbag chair is filled with beads, first identify the sample space.

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

The probability that a randomly selected beanbag chair is made from suede given that the beanbag chair is filled with beads 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 beanbag chair is made from suede and is filled with beads". Look at the table to see how many beanbag chairs are made from suede and are filled with beads.

	Foam	Beads
Velvet	4	5
Suede	3	4

The number of beanbag chairs that are made from suede and are filled with beads is 4.

Find the number of outcomes in the event

is the event "the beanbag chair is filled with beads", so look at the table to see how many beanbag chairs are filled with beads.

	Foam	Beads
Velvet	4	5
Suede	3	4

The number of beanbag chairs that are filled with beads 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 beanbag chair is made from suede given that the beanbag chair is filled with beads is

Looking for more? Try these:

Lesson: Conditional probability

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Teacher tools

Work it out

Not feeling ready yet? These can help:

OO.5Find probabilities using two-way frequency tables

OO.8Find conditional probabilities

Lesson: Conditional probability

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