IXL - Find probabilities using the addition rule (Algebra 2 practice)

Ivan attended his town's annual Worm Charming Competition. Contestants are assigned to a square foot of land, where they have 30 minutes to "charm" worms to the surface of the dirt. Ivan observed contestants' charming techniques and kept track of how many worms surfaced.

The probability that a contestant tried tapping the ground is 0.3, the probability that a contestant charmed over 30 worms is 0.5, and the probability that a contestant tried tapping the ground and charmed over 30 worms is 0.2.

What is the probability that a randomly chosen contestant tried tapping the ground or charmed over 30 worms?

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

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question

Emilio just returned from a spring break volunteer trip. He is shopping for a photo album that will showcase his photos from the trip. The albums range in photo capacity and orientation.

The probability that a photo album holds under 200 photos is 0.7, the probability that it is oriented horizontally is 0.3, and the probability that it holds under 200 photos and is oriented horizontally is 0.2.

What is the probability that a randomly chosen photo album holds under 200 photos or is oriented horizontally?

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 photo album holds under 200 photos" and

be the event "the photo album is oriented horizontally".

It is given that

(

)

0.7

(

)

0.3

and

(

A and B

)

0.2

Use the Addition Rule to find

(

A or B

)

the probability that a photo album holds under 200 photos or is oriented horizontally.

(

A or B

)

(

)

(

)

–

(

A and B

)

0.7

0.3

–

0.2

0.8

So,

(

A or B

)

0.8

Looking for more? Try these:

Lesson: Compound probability

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Not feeling ready yet? These can help:

Theoretical probability

Lesson: Compound probability

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