IXL - Find probabilities using the addition rule (Precalculus practice)

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

The probability that a cup contains pineapple juice is 0.7, the probability that it contains a regular straw is 0.6, and the probability that it contains pineapple juice and contains a regular straw is 0.4.

What is the probability that a randomly chosen cup contains pineapple juice or contains a regular straw?

Write your answer as a whole number, decimal, or simplified fraction.

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Learn with an example

question

Curious about people's recycling behaviors, Mitchell put on some gloves and sifted through some recycling and trash bins. For each type of plastic, he recorded how many bottles there were and whether they were correctly sorted.

The probability that a bottle is made of plastic #2 is 0.9, the probability that it was incorrectly sorted is 0.3, and the probability that it is made of plastic #2 and was incorrectly sorted is 0.2.

What is the probability that a randomly chosen bottle is made of plastic #2 or was incorrectly sorted?

Write your answer as a whole number, decimal, or simplified fraction.

key idea

Addition Rule of Probability

For events

and

the Addition Rule relates

(

C or D

)

and

(

C and D

)

(

C or D

)

(

)

(

)

–

(

C and D

)

This equation can be visualized using a Venn diagram:

(subtract to prevent double-counting)

solution

Let

be the event "the bottle is made of plastic #2" and

be the event "the bottle was incorrectly sorted".

It is given that

(

)

0.9

(

)

0.3

and

(

A and B

)

0.2

Use the Addition Rule to find

(

A or B

)

the probability that a bottle is made of plastic #2 or was incorrectly sorted.

(

A or B

)

(

)

(

)

–

(

A and B

)

0.9

0.3

–

0.2

So,

(

A or B

)

Looking for more? Try these:

Lesson: Compound probability

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Teacher tools

Work it out

Not feeling ready yet? These can help:

CC.1Calculate probabilities of events

Lesson: Compound probability

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