Prove that P __n i=1 Ai _ _n i=1 P(Ai )

Chapter , Problem 8

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QUESTION:

Prove that

                        \(P\left(\bigcup_{i=1}^{n} A_{i}\right) \leq \sum_{i=1}^{n} P\left(A_{i}\right)\)

Questions & Answers

QUESTION:

Prove that

                        \(P\left(\bigcup_{i=1}^{n} A_{i}\right) \leq \sum_{i=1}^{n} P\left(A_{i}\right)\)

ANSWER:

Step 1 of 3

To prove that

Let us prove the given inequality by mathematical induction.

Suppose, the given statement is denoted by i.e.,

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