Probability

# Probability - Probability The probability or likelihood of...

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Probability The probability or likelihood of an event is defined as total number of successes (or frequency of an event occurring) divided by the sample space (or total number of possible times for the event to occur.) For example, the probability of rolling an even number on a standard six-sided die is 3/6 = ½ because there are six possible outcomes (1,2,3,4,5,6) of which three are even. It is IMPORTANT to note that each of the outcomes in the sample space MUST be equally probable for this definition to be valid. For example, if rolling a 1 was 5 times more likely than each of a 2, 3, 4, 5, or 6, then ½ would not be the answer to the question above. We can denote the probability of an event A occurring as p(A).

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Some probability rules: 1) The sum of the probabilities of all events/outcomes occurring is always 1. (Each event/outcome must be disjoint.) 2) The probability of any event is in between 0 and 1, inclusive. 3) If two events A and B are disjoint, then the probability of either event occurring is the sum of the probability of A occurring and of B occurring. Symbolically, we have, if p(A B) = 0, then p(A B) = p(A)+p(B). 4) If two events are independent, meaning that one event does not affect the probability of another occurring, such as two consecutive flips of a fair coin, then the probability of both occurring is the
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Probability - Probability The probability or likelihood of...

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