Step-by-step explanation:
I suppose the answer is yes.
In the axiomatic form of probability from (Ω,F,P) , the probability measure is defined as
[tex] \bold {P:F \rightarrow[0,1] }[/tex]
As you see, the co-domain of the map does not exclude the irrational numbers.
As an example, imagine
When you calculate the probability, the denominator will usually have a π .
Unless the numerator has a π as well, the probability will be irrational.
A more readily available example is the cumulative distribution function of a Gaussian variable.
A famous example is Buffon's needle. A needle is tossed randomly onto a horizontal plane ruled with parallel lines whose distance apart is the same as the length of the needle. The probability that the needle crosses a line is 2/π.
Hope it is Helpful to you
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Answers & Comments
Step-by-step explanation:
I suppose the answer is yes.
In the axiomatic form of probability from (Ω,F,P) , the probability measure is defined as
[tex] \bold {P:F \rightarrow[0,1] }[/tex]
As you see, the co-domain of the map does not exclude the irrational numbers.
As an example, imagine
When you calculate the probability, the denominator will usually have a π .
Unless the numerator has a π as well, the probability will be irrational.
A more readily available example is the cumulative distribution function of a Gaussian variable.
Yes we can have irrational probability.
A famous example is Buffon's needle. A needle is tossed randomly onto a horizontal plane ruled with parallel lines whose distance apart is the same as the length of the needle. The probability that the needle crosses a line is 2/π.
Hope it is Helpful to you