Roll a dice, ignore result if result is maximum value

Question

Let's say I have a six-faced dice, but I only want results between $1$ and $5$.

One way to do that would be to roll a ten-faced dice and divide the result by two ($1-2$ becomes $1$, $3-4$ becomes $2$, and so on).

Another way would be to roll a six-faced dice and if six is obtained, roll the dice again (until the result is less than six).

The idea is to maintain equiprobability of course!

The two methods would seem similar in terms of probability but we had an argument about entropy ; using the second method, if I roll six first, would the second result be affected by the fact that I already rolled the dice? Would the two methods be absolutely the same in terms of probability?

Answer 1

Assuming its a fair die (dice is the plural of die) then the outcome of any roll does not depend on its previous history.

I you roll a six your first roll the chances you get a six on the next is still $\frac{1}{6}$.

If you choose to roll a ten sided dice counting 1-2 as 1 for example or roll a six sided dice and ignore sixes you will still get the result: 1,2,3,4,5 with equal randomness.

That is if you do it long enough you will have approximately the same number of each.

Answer 2

It's just like asking of a couple had 10 boys what's the probability that the 11th lid will also be a boy!The probability will be 50%.

The knowledge of previous events will not effect of the next one of you're sure that the event is not dependent on the previous events.

And as far as the equiprobability is concerned, the two will have equal probability. The six faced die has only five outcomes as far as you're concerned and all those five have the same probability. so each has prob of 1/5. same as that of a 10 faced die!

Answer 3

The only difference between the 2 methods is that the sixfaced dice might(and most probably will) take more throws to get the same amount of results.

The probability for both approaches will be the same and your previous throw will not affect your last throw. Assuming both you and the dice are fair ;).