contestada

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

Write down an expression for the probability that Paul does not win.

Respuesta :

Answer:

[tex]1 - p[/tex]

Step-by-step explanation:

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

[tex]\mathbb{P}(A) + \mathbb{P}(\Omega \setminus A) = \mathbb{P}(\Omega) = 1[/tex].

So

[tex]\mathbb{P}(\Omega \setminus A) = 1 - \mathbb{P}(A) = 1 - p[/tex].

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

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