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

A health instructor surveyed all her students, and tallied the results. The first survey question asked, "Do you adhere to a vegetarian diet or omnivorous diet?" The second question asked, "Approximately how often do you exercise?"

	A vegetarian diet	An omnivorous diet
Daily	2	1
Weekly	4	3

What is the probability that a randomly selected student exercises daily and adheres to an omnivorous diet?

Simplify any fractions.

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Learn with an example

question

A birthday party caterer counted the number of juice cups on the table. The cups contained different flavored juices and different shaped straws.

	Heart-shaped straw	Star-shaped straw
Orange juice	5	4
Grape juice	6	3

What is the probability that a randomly selected cup contains orange juice and contains a star-shaped straw?

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 cup contains orange juice" and

be the event "the cup contains a star-shaped straw".

To find the probability that a cup contains orange juice and contains a star-shaped straw, first identify the sample space and the event.

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

The event is

and

"the cup contains orange juice and contains a star-shaped straw".

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 cup contains orange juice and contains a star-shaped straw", so look at the table to see how many cups contain orange juice and contain a star-shaped straw.

	Heart-shaped straw	Star-shaped straw
Orange juice	5	4
Grape juice	6	3

The number of cups that contain orange juice and contain a star-shaped straw is 4.

Find the total number of outcomes.

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

	Heart-shaped straw	Star-shaped straw
Orange juice	5	4
Grape juice	6	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 cup contains orange juice and contains a star-shaped straw 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:

AA.1Theoretical and experimental probability

JJ.1Probability of simple events

Lesson: Two-way tables

Lesson: Probability

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