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Probability Rules

Understand the fundamental principles of probability with rules ranging from defining probabilities for events to calculating joint probabilities and conditional events. Learn how to apply these rules effectively for accurate outcomes in statistical analysis.

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Probability Rules

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  1. Probability Rules • Rule 1. The probability of any event (A) is a number between zero and one. 0 < P(A) < 1

  2. Probability Rules • Rule 2. The sum of the probabilities of all basic outcomes in the sample space must equal one P(S)=P(e1)+P(e2)+P(e3)+....+P(en)=1

  3. Probability Rules • Rule 3. The probability of the union of two basic outcomes is equal to the sum of the probabilities of the individual events If E1 = (e1, e2, e3) then, P(E1) = P(e1) + P(e2) + P(e3)

  4. Probability Rules • Rule 4. The Complement of an event is the remainder of the sample space beyond the event P (A) = 1 - P (A)

  5. Probability Rules • Rule 5. The Addition Rule describes the probability for the union of two events as the sum of marginal probabilities minus their joint (common) probability P(A or B) = P(A) + P(B) - P(A and B)

  6. Probability Rules • Rule 6. Addition Rule for mutually exclusive events A and B P(AUB) = P(A) + P(B) P(A or B) = P(A) + P(B)

  7. Probability Rules • Rule 7. Conditional probability for any two events, A and B, is P (A given B) = P (A and B) / P (B) where, P (B) is not equal to zero

  8. Probability Rules • Rule 8. Conditional probability for independent events, A and B, is P (A \ B) = P (A), and P (B \ A) = P (B)

  9. Probability Rules • Rule 9. Multiplication rule for two Events, A and B, is P (A and B) = P (A) * P (B \ A), or P (B and A) = P (B) * P (A \ B)

  10. Probability Rules • Rule 10. Multiplication rule for independent events, A and B, is P (A and B) = P (A) * P (B)

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