What is P ( A &#x222A;<!-- ∪ --> ( B &#x2229;<!-- ∩ --> C ) ) ?

hisyhauttaq84w 2022-05-09 Answered
What is P ( A ( B C ) )?

The question says it all. I know
P ( A ( B C ) ) = P ( A B ) + P ( A C ) .
Would this mean,
P ( A ( B C ) ) = P ( A B ) + P ( A C ) ?
Just want to make sure.
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Answers (1)

Gillian Kelly
Answered 2022-05-10 Author has 11 answers
The equation
P ( A ( B C ) ) = P ( A B ) + P ( A C )
will almost certainly not hold. This is because
P ( A ( B C ) ) = P ( ( A B ) ( A C ) ) P ( A B )
and similarly
P ( A ( B C ) ) P ( A C ) .
For the stated equation to hold, both P ( A B ) and P ( A C ) would have to be zero, showing that
P ( A ) = P ( B ) = P ( C ) = 0.
However, if this condition is satisfied, then the stated equation will hold.
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