You are told that: 1. P ( P ) = 0.15 2. P ( T <mrow class="M

Villaretq0

Villaretq0

Answered question

2022-06-15

You are told that:
1. P ( P ) = 0.15
2. P ( T | P ) = 0.91
3. P ( T | ¬ P ) = 0.04
4. P and T are not independent.

Whats P ( T )?

I've been really struggling with this one. I've tried substituting a bunch of stuff into the multiplication rule
P ( A B ) = P ( A ) P ( B | A )
and the addition rule
P ( A B ) = P ( A ) + P ( B ) P ( A B ) .
I've also tried drawing a conditional probability tree to help me see what's going on, but I just don't seem to be getting anywhere.

Answer & Explanation

lorienoldf7

lorienoldf7

Beginner2022-06-16Added 19 answers

P ( T ) = P ( T P ) + P ( T P c ) = P ( T | P ) P ( P ) + P ( T | P c ) P ( P c ) = P ( T | P ) P ( P ) + P ( T | P c ) [ 1 P ( P ) ]
[I have typed A c for the complement of A].

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