practice_problems/problems/unit-01/A-outcome-spaces-and-events/2

[giscus[bot]]

practice_problems/problems/unit-01/A-outcome-spaces-and-events/2

https://mids-w203.github.io/practice_problems/problems/unit-01/A-outcome-spaces-and-events/2.html

[HafeziDS]

The proof presented is based on a proof by contradiction.

[karan-mids24]

Will this be a correct way to prove?
Let 'n' be the number of outcomes in the sample space Ω
2ⁿ = ∞
Hence, n = log₂(∞) = ∞ (The logarithm of ∞ to any positive base greater than 1, is ∞.)

Hence, the sample space Ω must have infinitely many outcomes.

[bryan-md]

Let S = the outcome space and P(S) be the event space (power set of S)
The definition of the power set of S:
P(S) = 2ⁿ , where n = |S| , the number of elements in the outcome space

Therefore if the Event Space has infinitely many outcomes, than the Sample Space must have infinitely many outcomes.