Math formula question

[Dynasoft]

If you still argue, here's a really simple version you can repeat 100 times to get experimental probabilities:
Flip a coin
If tails, flip again.
Record whether you got heads, tails+heads, or tails+tails.

If you're right, the three outcomes should all be equally likely, and you should get around 30 of each. If I'm right, you should get around 50 heads, and around 25 tails+heads, and around 25 tails+tails.

[MuddyMole]

Logically speaking, the third dice has only 3 sides - the physical shape of the dice is irrelevant. Since rolling a 1 on the third dice is logically impossible, we could choose to disregard that dice altogether.
If you wanted to, you can include it anyway, but it doesn't change anything:

P = 1 - ((1-0.25) * (1-0.125) * (1-0))

is exactly the same as

P = 1 - ((1-0.25) * (1-0.125))

I'm bored of this discussion now...

[droberson]

Dynasoft, you and agree given how the experiment (game) is defined. I don't disagree with that.

[Jax]

Just to chime in here, possibly to add confusion, a probability of zero does not mean an event is impossible, in general. Indeed, such events are called 'almost impossible' rather than 'impossible' to reflect this. (Likewise, 1 is called 'almost certain' rather than 'certain')

However, this is not important for the current discussion, since the probability spaces are countable. But a little fact none the less!