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Conditional Probability - Concept

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Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

Conditional probability is the probability of some event, given the occurrence of another event. Conditional probability is often written as P (A l B) and is defined as the probability of A and B occurring together, divided by the probability of A. This concept is often used in scientific experiments.

Conditional probability is probability that we're looking at when we're given 1 outcome already has occurred and we're trying to find another outcome. Okay so imagine you are running in a race, okay and you can say okay fine the probability you won gold giving you place in the top 3 okay. The probability of that event is actually going to be higher than you placing first overall without knowing that you're in the top 3 because you could've placed in any sort of realm with that conditional with that conditional statement what you're really doing is sort of narrowing down the window that you're looking at.
And there's a formula for calculating conditional probability and what it is, is it's probability b in this little line and basically what this is saying is b given a so what we're told is that event a has already occurred and we're trying to find the probability of that event b happens as well. Okay so probability of b given event a has happened so this would be okay finding probability you win gold giving you a place in the top 3 is equal to the probability of both events occurring so the probability of gold and top 3 over the probability of just the given, so probability over top 3. Okay it looks a little bit complicated on the surface but really if you can just remember this formula it's pretty straight forward and how you actually use it.
Okay sometimes what you see is multiplication, you can multiply both sides by the probability of a and so what you end up with is a probability of a times the probability of b given a is equal to the probability of a and b, perfectly fine just standard numeric multiplication, this is just a number you can cross multiply and the statement will still be true. Okay so the general form for conditional probability probably probability of given a is equal the probability of a and be over the probability of a.

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