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@@ -504,18 +504,15 @@ Probability is often associated with at least one event. This event can be anyth
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#### Marginal Probability:
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If A is an event, then the marginal probability is the probability of that event occurring, P(A).
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##### Example:
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Assuming that we have a pack of traditional playing cards, an example of a marginal probability would be the probability that a card drawn from a pack is red: P(red) = 0.5.
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**Example:** Assuming that we have a pack of traditional playing cards, an example of a marginal probability would be the probability that a card drawn from a pack is red: P(red) = 0.5.
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#### Joint Probability:
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The probability of the intersection of two or more events. Visually it is the intersection of the circles of two events on a Venn Diagram (see figure below). If A and B are two events then the joint probability of the two events is written as P(A ∩ B).
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##### Example:
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The probability that a card drawn from a pack is red and has the value 4 is P(red and 4) = 2/52 = 1/26. (There are 52 cards in a pack of traditional playing cards and the 2 red ones are the hearts and diamonds). We’ll go through this example in more detail later.
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**Example:** The probability that a card drawn from a pack is red and has the value 4 is P(red and 4) = 2/52 = 1/26. (There are 52 cards in a pack of traditional playing cards and the 2 red ones are the hearts and diamonds). We’ll go through this example in more detail later.
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#### Conditional Probability:
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The conditional probability is the probability that some event(s) occur given that we know other events have already occurred. If A and B are two events then the conditional probability of A occurring given that B has occurred is written as P(A|B).
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##### Example:
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The probability that a card is a four given that we have drawn a red card is P(4|red) = 2/26 = 1/13. (There are 52 cards in the pack, 26 are red and 26 are black. Now because we’ve already picked a red card, we know that there are only 26 cards to choose from, hence why the first denominator is 26).
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**Example:** The probability that a card is a four given that we have drawn a red card is P(4|red) = 2/26 = 1/13. (There are 52 cards in the pack, 26 are red and 26 are black. Now because we’ve already picked a red card, we know that there are only 26 cards to choose from, hence why the first denominator is 26).
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