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1) P(A) ≥ 0
2) P(Sample Space) = 1
3) If A and B are disjoint, P(A U B) = P(A) + P(B)
FYI: disjoint means there are no components in common
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Roll a fair die
A = The roll is even = {2, 4, 6} P(A) = 3/6
B = The roll is at least 4 = {4, 5, 6} P(B) = 3/6
A U B = {2, 4, 5, 6} P(A U B) = 4/6
Axium 3 : P(A U B) = P(A) + P(B) is not true because A and B is NOT disjoint.
General formula: for any A, B : P(A U B) = P(A) + P(B) - P(A ∩ B)
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- P(A) + P(A') = 1
- 0 ≤ P(A) ≤ 1
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Where do probabilities come from?
1) Experimental results to estimate them
- survey
- flipped thumbtacks to count point up
2) Counting equally probable events
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Covered sections 2.1 and 2.2
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