Concepts of Probability
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| show | -The experiment can have more than one possible outcome.
-Each possible outcome can be specified in advance.
-The outcome of the experiment depends on chance.
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| show | A coin toss has all the attributes of a statistical experiment. There is more than one possible outcome. We can specify each possible outcome (i.e., heads or tails) in advance. And there is an element of chance, since the outcome is uncertain.
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| show | A sample space is a set of elements that represents all possible outcomes of a statistical experiment.
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| show | A sample point is an element of a sample space.
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| What is an event? * | show 🗑
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| What is an example of an event? | show 🗑
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| show | 1. Mutually exclusive
2. Independent
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| When are events mutually exclusive? * | show 🗑
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| show | Two events are independent when the occurrence of one does not affect the probability of the occurrence of the other.
Ex. If i roll a dice twice, the first roll does not influence the second roll.
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| What is a null/empty set? | show 🗑
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| show | A set is a well-defined collection of objects.
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| show | Each object in a set is called an element of the set.
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| show | Two sets are equal if they have exactly the same elements in them. The order of the elements does not matter.
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| What is a subset? * | show 🗑
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| show | A set is usually denoted by a capital letter, such as A, B, or C.
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| show | An element of a set is usually denoted by a small letter, such as x, y, or z.
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| show | The null set is denoted by {∅}
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| What is a union?* | show 🗑
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| show | U
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| show | The intersection of two sets is the set of elements that are common to both sets. Thus, set W is the intersection of sets X and Y. If W = {2}; X = {1, 2}; Y= {2, 3, 4}; and Z = {1, 2, 3, 4}.
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| show | Symbolically, the intersection of X and Y is denoted by X ∩ Y. An arch. An upside-down u.
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| show | Fortunately, there are ways to make the counting task easier. There are three rules of counting that can save both time and effort - event multiples, permutations, and combinations.
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| What is an event multiple? * | show 🗑
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| show | -The probability of any sample point can range from 0 to 1. -The sum of probabilities of all sample points in a sample space is equal to 1.
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| What is the probability of an event? | show 🗑
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| show | The idea that the relative frequency of an event will converge on the probability of the event, as the number of trials increases, is called the law of large numbers. Frequencey Event/# of trials.
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| When are two events mutually exclusive or disjoint? | show 🗑
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| What is conditional probability? | show 🗑
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| What is the complement of an event? | show 🗑
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| show | The probability that Events A and B both occur is the probability of the intersection of A and B. The probability of the intersection of Events A and B is denoted by P(A ∩ B). If Events A and B are mutually exclusive, P(A ∩ B) = 0.
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| show | The probability that Events A or B occur is the probability of the union of A and B. The probability of the union of Events A and B is denoted by P(A ∪ B) .
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| show | If the occurence of Event A changes the probability of Event B, then Events A and B are dependent.
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| show | On the other hand, if the occurence of Event A does not change the probability of Event B, then Events A and B are independent.
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| show | The probability that event A will occur is equal to 1 minus the probability that event A will not occur. P(A) = 1 - P(A')
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| show | The probability that Events A and B both occur is equal to the probability that Event A occurs times the probability that Event B occurs, given that A has occurred.
P(A ∩ B) = P(A) P(B|A)
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| What is the rule of addition? | show 🗑
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| show | Note: Invoking the fact that P(A ∩ B) = P( A )P( B | A ), the Addition Rule can also be expressed as
P(A ∪ B) = P(A) + P(B) - P(A)P( B | A )
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Created by:
Colin Reeder