Probability Properties

P0

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Answer explanation

The probability of event E is greater than or equal to 0 since it is the sum of non-negative numbers.

P1

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Answer explanation

The probability of omega is 1 because it adds up the probabilities of all the outcomes in the space.

P4

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Answer explanation

The probability of the complement of E is 1 minus the probability of E. Think counting complementarily.

P5

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Answer explanation

This is a sum with no terms!

P2

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Answer explanation

This is called the addition rule. It works because A intersects B = empty set.

P3

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Answer explanation

This is called monotonicity. It is similar to set cardinality.

P6

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Answer explanation

This is called inclusion-exclusion and is similar to PIE for two sets.

P7

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Answer explanation

This is called union bound. It follows from immediately from P6.

In P6 we are subtracting from the sum of Pr[A] and Pr[B] so it will be less than or equal to (if A intersects B = 0) the sum of Pr[A] and Pr[B].

• P7

• P6

• P2

• P3

• P0

• P7

• P6

• P2

• P3

• P5