Probabilities - The Likelihood Of Events

**Strings (S _{i}P_{j}A_{jk}) = S_{7}P_{6}A_{64} Base Sequence = 12735 String Sequence = 12735 - 6 - 64 **

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Probabilities - The Likelihood Of Events

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Figure 118.3 is a Venn Diagram for events A and B. Given the following information:

Probability of A union B = P[A ∪ B] = 0.7

Probability of A union B' = P[A ∪ B'] = 0.9. B' is the complement of B.

Probability of A = P[A].

Probability of B = P[B].

Determine P[A].

**The strings**:
S_{7}P_{6}A_{64} (Grouping - Multi-criteria).
**The math**:

Pj Problem of Interest is of type *grouping* (multi-criteria). *Grouping* is at the heart of statistics. The grouping may be permutational or combinational, single criterion or multi-criteria grouping.

Formulas of Interest

P[A ∪ B] = P[A] + P[B] - P[A ∩ B]

P[A ∪ B'] = P[A] + P[B'] - P[A ∩ B']

So, P[A] + P[B] - P[A ∩ B] = 0.7 ------------------(1)

So, P[A] + P[B'] - P[A ∩ B'] = 0.9 -----------------(2)

P[A ∩ B'] = P[A] - P[A ∩ B]

P[B'] = 1 - P[B]

So, equation (2) becomes:

P[A] + 1 - P[B] - P[A] + P[A ∩ B] = 0.9

So, 1 - P[B] + P[A ∩ B] = 0.9 ------------------------(3)

Adding equations (1) and (3) we have:

P[A] + P[B] - P[A ∩ B] + 1 - P[B] + P[A ∩ B] = 1.6

So, P[A] = 0.6

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

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The Universe is composed of *matter* and *radiant energy*. *Matter* is any kind of *mass-energy* that moves with velocities less than the velocity of light. *Radiant energy* is any kind of *mass-energy* that moves with the velocity of light.

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