IXL - Independence and conditional probability (Geometry practice)

In an experiment, the probability that event

occurs is

and the probability that event

occurs is

and

are independent events, what is the probability that

and

both occur?

Simplify any fractions.

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Learn with an example

question

In an experiment, the probability that event

occurs is

and the probability that event

occurs is

and

are independent events, what is the probability that

and

both occur?

Simplify any fractions.

key idea

A sample space is a set of possible

outcomes.

An event is a set of outcomes in a sample space. If

is an event, then

(

)

is the probability that

occurs.

The definition of independence states that

and

are independent events if and only if

(

and

)

(

)

(

)

solution

It is given that

(

)

and

(

)

Since

and

are independent, the probability that

and

both occur is the product of their individual probabilities.

(

and

)

(

)

(

)

So, the probability that events

and

both occur is

Looking for more? Try these:

Lesson: Compound probability

Lesson: Conditional probability

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Teacher tools

Work it out

Not feeling ready yet? These can help:

AA.11Find conditional probabilities

AA.10Identify independent events

Lesson: Compound probability

Lesson: Conditional probability

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