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Probability values are between... |
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Probabilities or expected frequencies of an event sum up to... |
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ONE
P(1) + P(2)+P(3)+...+P(n) = 1 |
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the occurrence of one event has no influence on the occurrence of the other event |
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when to use multiplication rule |
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when the probability uses the word and
P(A and B) = P(A) x P(B) |
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The probability of independent events occurring together |
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the product of their separate probabilities.
P(4 and Tail) = P(4) x P(Tail) = 1/6 x 1/2 = 1/12. |
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Non-overlapping, which means the two events cannot both occur at the same time |
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when to use the addition rule |
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when the probability uses the word or
P(A or B) = P(A) + P(B) |
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The probability that either event A or event B will occur |
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the sum of their separate probabilities.
P(Even) = P(2) or P(4) or P(6) P (Even) = P(2) + P(4) + P(6) = 1/6 + 1/6 + 1/6 = 1/2 |
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The probability that either event A or event B will occur when mutually exclusive |
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when 2 events have one or more outcomes in common |
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probability of event A and event B occurring when they're non-mutually exclusive |
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P(A or B)=P(A) + P(B)-P(A and B) |
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our estimate of the probability on an event B will be modified based on partial information that we have or because we know a particular event A has taken place |
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the probability of B given A, where the '|' means 'given' |
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the probability of B given A |
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P(B | A)
the '|' means 'given' |
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P(B | A) if A and B are independent |
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P(B | A) if A and B are mutually exclusive |
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probability of both A and B occurring when A and B are dependent |
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Baye's theorem for conditional probabilities |
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P(B | A ) = P(A and B)/P(A)
P(Second|First)=P(First and Second)/P(First) |
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modified Baye's theorem for conditional probabilities (one that makes sense to me) |
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The probability of obtaining exactly n successes in N trials is given by... |
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the limit of binomial distribution |
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the binomial expression when n = 2 |
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Definition
(p + q)2 = p2 + 2pq + q2 = 1
p and q represent mutually exclusive events |
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the binomial expression when n > 2, in this case, n = 5 |
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Definition
(p + q)5 = p5 + 5p4q1 + 10p3q2 + 10p2q3 + 5p1q4 + q5 |
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what does each letter in this equation represent? [image] DRAW THIS! |
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Definition
p = probability of dominant q = probability of recessive N = number of times k = number of dominants being tested for N-k = expected number of recessives |
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