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vodomira [7]
3 years ago
7

Consider three events A, B and C with following properties.

Mathematics
1 answer:
lisov135 [29]3 years ago
5 0
By the inclusion/exclusion principle,

\mathbb P(D)=\mathbb P(A\cup B\cup C)
\mathbb P(D)=\mathbb P(A)+\mathbb P(B)+\mathbb P(C)-\bigg(\mathbb P(A\cap B)+\mathbb P(A\cap C)+\mathbb P(B\cap C)\bigg)+\mathbb P(A\cap B\cap C)
\mathbb P(D)=\dfrac14+\dfrac16+\dfrac14-\dfrac39+\dfrac1{13}
\mathbb P(D)=\dfrac{16}{39}\neq1

So the union of A, B, and C does not constitute the entire sample space.
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