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What is the difference between the product rule for independent and dependent events?

User Codrelphi
by
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1 Answer

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Independent Events The probability of one event happening isn't influenced by the outcome of another.
In mathematical terms
A
,
B
events
,
P
(
A

B
)
=
P
(
A
)

P
(
B
)

This reads: Probability of A and B happening is equal to the probability of A happening multiplied by the probability of B happening
An equivalent definition
P
(
A

B
)
=
P
(
A
)
This reads: The probability of A given B happened is equal the probability of A
Example:
Event A: Rolling a number larger than four on a die in the first roll Event B: Rolling a 6 on a die on the second roll. These events are independent because one roll of a dice doesn't influence the outcome of another dice roll.
Dependent Events Is the oposite.If the outcome of one event influences the probability of the other they aren't independent
P
(
A

B
)

P
(
A
)
Example:
Event A: Rolling a number larger than four on a die Event B: Rolling a 6 on a die on the same roll. These events are dependent because ,as we are in the same dice roll, the occurrence of event B changes the probability of event A, actually it makes it 1.
User Emiliya
by
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