Probabilities - The Likelihood Of Events
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Probabilities - The Likelihood Of Events 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: S7P6A64 (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

Math

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