# Question: Develop a careful proof of Theoram 2 1 which states that

Develop a careful proof of Theoram 2.1 which states that for any events A and B,

Pr (A U B) = Pr (A) + Pr (B) – Pr (A ∩ B).

One way to approach this proof is to start by showing that the set can be written as the union of three mutually exclusive sets,

And hence by Corollary 2.1,

Next, Show that

And likewise

Put these results together to complete the desired proof.

Pr (A U B) = Pr (A) + Pr (B) – Pr (A ∩ B).

One way to approach this proof is to start by showing that the set can be written as the union of three mutually exclusive sets,

And hence by Corollary 2.1,

Next, Show that

And likewise

Put these results together to complete the desired proof.

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