practice_problems/problems/unit-01/A-outcome-spaces-and-events/1

[giscus[bot]]

practice_problems/problems/unit-01/A-outcome-spaces-and-events/1

https://mids-w203.github.io/practice_problems/problems/unit-01/A-outcome-spaces-and-events/1.html

[soyaddan]

Ω ={ABC,CBA,BAC,ACB,BCA,CAB) hence the number of events would be 2 (power of 6) = 64

[marcosgeraldo-berkeley]

The cardinality of Omega is given by all the way we can pic the three children.
#Ω = 3! = 6
The cardinality of S is { null, 6 over 1, 6 over 2, ... Ω} which is (1 + 1)^6
#S = 2^6 = 64

[mbparacha88]

Question here, according to https://byjus.com/maths/power-set/#:~:text=The%20power%20set%20is%20a,formed%20for%20a%20given%20set., the power set calculation will be 2^3, but I am assuming given order does not matter, it can be. 2^6?

[bryan-md]

Thanks for this question and link, it helped me understand the nuance of a power set.
To my understanding is the power of any set, is the set of all subsets. 2^n, where n = the number of elements in the set.

In the question above, the direction "taking the event space to be the power set" would mean a power set of the SAMPLE SPACE. The sample space here is 6 , the sample space = {ABC,CBA,BAC,ACB,BCA,CAB)

In the link you gave - the set A = {a,b,c}, so n = 3. 2^n = 8.

The difference is that an element in the sample space in the practice problem is "ABC", the element in set A here is 'a'.

In the practice problem each of the kids "Allison" is an element of an outcome, not an outcome itself.

[mabehrnyc]

How important is the notation here? If we submitted {ABC,ACB} or ((A,B,C),(A,C,B)) on a test instead of {(A,B,C),(A,C,B)}, would we lose points?