Hi Team

I have doubt regarding Set of events Vs Set of possible outcomes.In Week 18,“Probability Recap”,sir mentioned below points

Omega : Set of Possible outcomes

F: Set of events

p:maps events to probability

If Die has only 3 faces(1,2,3) and is rolled twice,I am interested in events where no 3 has occurred in outcome with order ignored

omega :(1,1),(1,2),(1,3),(2,2),(2,3),(3,3)

F:(1,1),(1,2),(2,2)

p :How should I calculate my probability of each event.Below is my calculation

(1,1) —1/9

(1,2) --2/9

(2,2) --1/9

Probabilities has to be calculated from set of all possibile outcomes(Omega) and not F

my random variable X :Sum of outcomes and below is the PMF

```
2 -→1/9
3 -→2/9
4 -→1/9
```

But above is not summing up to 1.Instead if I say that my event space(F) has only 4 outcomes and modify the probabilities as below ,ie.,calculation prob from F and not Omega,r.v X sums to 1

```
(1,1) ---¼
```

(1,2) --2/4

(2,2) --¼

But above cant be true as prob of getting (1,1) for 3 faced die is 1/9.

And I am not sure if sir has discussed probability calculations for an example where Omega is not equal to F.

Please let me know If am missing anything

Regards

Subbu