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Instructor: Welcome back everybody.
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So far we've only talked about events
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and the theoretical probability
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of which remains unaffected by other events.
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We call these independent, and the simplest example
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is flipping a coin.
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You always have a 50% chance of getting tails
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regardless of the result obtained with the previous throw.
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In addition, we can have dependent events.
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Their probabilities vary as conditions change.
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For instance, take the probability
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of drawing the queen of spades.
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Normally the answer is 1 over 52
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since we have exactly one favorable outcome
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and 52 elements in the sample space.
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Now, imagine we know that the card we drew was a spade.
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Our chances of getting the queen of spades suddenly go up
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since the new sample space contains
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the 13 cards from the suit only.
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Therefore, the probability becomes 1 over 13.
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Okay, now imagine a different scenario.
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Instead of a spade, we know our card is a queen
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so the sample space only consists of four cards.
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Therefore, the probability of drawing
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the queen of spades becomes 1 over 4.
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With this example, you could clearly see how the probability
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of an event changes depending on the information we have.
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This is a very important insight relating
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to this whole section.
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Okay, before we move on, let's introduce some new notation.
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As usual, suppose we have two events, A and B,
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to express the probability of getting A,
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if we are given that B has occurred.
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We use the following notation, P(A|B).
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We read this as P of A given B.
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Going back to our card example,
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event A is drawing the queen of spades
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and event B is drawing a spade.
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Therefore, P of A given B would represent
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the probability of drawing the queen of spades,
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if we know the card is a spade.
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We already calculated this earlier,
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so P of A given B equals 1 over 13.
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Similarly, if event C represents getting a queen
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then P of A given C expresses the likelihood
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of getting the queen of spades, assuming we drew a queen.
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Thus, P of A given C equals 1 over 4.
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Perfect, we call this probability
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the conditional probability, and we use it
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to distinguish dependent from independent events.
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In the next lecture, we are going to show you
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how to compute it and interpret conditional probabilities.
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Thanks for watching.
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