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vagabundo [1.1K]
3 years ago
15

The probability that Paul wins in a raffle is given by the expression

Mathematics
1 answer:
AnnZ [28]3 years ago
4 0

Answer:

1 - p

Step-by-step explanation:

Consider the (\Omega, \mathcal{F}, \mathbb{P}) where \mathcal{F} is sigma algebra and \mathbb{P} is probabilistic measure. Denote A \subset \Omega where Paul wins. By additivity of measure we know that

\mathbb{P}(A) + \mathbb{P}(\Omega \setminus A) = \mathbb{P}(\Omega) = 1.

So

\mathbb{P}(\Omega \setminus A) = 1 - \mathbb{P}(A) = 1 - p.

But \Omega \setminus A is exactly the set where Paul does not win. Q.E.D.

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