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The third postulate of probability is sometimes referred to as the special addi- tion rule; it is special in the sense that events A₁, A2, A3,..., must all be mutually exclusive. For any two events A and B, there exists the general addition rule, or the inclusion-exclusion principle: THEOREM 2.7. If A and B are any two events in a sample space S, then P(AUB) = P(A) + P(B) - P(ANB) 2.9. Use the formula of Theorem 2.7 to show that (a) P(ANB) ≤ P(A) + P(B); (b) P(ANB) = P(A) + P(B)-1.

The third postulate of probability is sometimes referred to as the special addi- tion rule; it is special in the sense that events A₁, A2, A3,..., must all be mutually exclusive. For any two events A and B, there exists the general addition rule, or the inclusion-exclusion principle: THEOREM 2.7. If A and B are any two events in a sample space S, then P(AUB) = P(A) + P(B) - P(ANB) 2.9. Use the formula of Theorem 2.7 to show that (a) P(ANB) ≤ P(A) + P(B); (b) P(ANB) = P(A) + P(B)-1.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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The third postulate of probability is sometimes referred to as the special addi- tion rule; it is special in the sense that events A₁, A2, A3,..., must all be mutually exclusive. For any two events A and B, there exists the general addition rule, or the inclusion-exclusion principle: THEOREM 2.7. If A and B are any two events in a sample space S, then P(AUB) = P(A) + P(B) - P(ANB) 2.9. Use the formula of Theorem 2.7 to show that (a) P(ANB) ≤ P(A) + P(B); (b) P(ANB) = P(A) + P(B) - 1. |
Transcribed Image Text:The third postulate of probability is sometimes referred to as the special addi- tion rule; it is special in the sense that events A₁, A2, A3,..., must all be mutually exclusive. For any two events A and B, there exists the general addition rule, or the inclusion-exclusion principle: THEOREM 2.7. If A and B are any two events in a sample space S, then P(AUB) = P(A) + P(B) - P(ANB) 2.9. Use the formula of Theorem 2.7 to show that (a) P(ANB) ≤ P(A) + P(B); (b) P(ANB) = P(A) + P(B) - 1. |
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