May I suggest you do your own homework?

Steephie, het is een eeuwigheid geleden dat ik kansrekening deed, maar misschien moet je 1 min de kans dat je geen enkele keer 6 gooit doen. Dat wil nog wel eens tot de goede oplossing leiden. Succes!

If you don't roll a 6 on your first 5 throws, then the next one is sure to be a 6, because you're due.

For that calculation, it's easier to assume you get NO 1s, and then subtract. To do this, multiply together the odds of getting a not-1 on each roll: 5/6 * 5/6 * 5/6 * 5/6 * 5/6 * 5/6. (This assumes a perfect die and that the throws have no impact on each other, which is a relatively fair assumption assuming you don't throw the die so hard it dents).

Each throw is independent. The chance of getting at least one six is equal to 1 minus the chance of getting no sixes:
1 - (5/6)^6

Listen to what Draugnar said.

Also, go to office hours if you don't understand.

You guys are giving him the answer to his homework.

Draugnar, if this was my homework I'd ask my teacher, but since that's quite a few grades up and I'm curious I figured I'd waste a few seconds of your time :)

everyone else: thanks for the answers!

So, the answer is 66,5%? I thought it would be much higher... Or did I do something wrong after all?

@Steephie - Sorry, I thought you were maybe taking probability and staistics. You are younger than I remember. And yes, the odds of not getting one are just over 33.489%

hehe, yeah, first time I'll be "taking" anything is the end of this year, and that's a very general direction...

Apology accepted though, I wasn't offended, no worries :)

Now, what are the odds of dealing out 13 cards from a standard poker deck (52 cards, no jokers) and not getting an Ace. This can be converted to a practical exercise as you can compute the odds of one of your opponents hitting a pair off the flop knowing that everyone in the table after the flop has 2 cards that could hit any one of the three cards (we won't take into account the possibility the board paired or that they may have hit a flush or a straight or that being in the hand to see the flop depending on the betting may indicate hand strength, etc.)

0.167%

The chance of getting a 6 is 0.167% no matter how many times you roll the dice.

And a hint, at a full table (10 players), pre flop, the odds are about 80% that someone will get an Ace. But heads up play (end of a tournament, two players battling it out), the odds are only 27.4% that one player will get an Ace. And if you have an ace, then the odds are 11.64% that your opponent will have one too.

@SYnapse - That is true on any given roll (well, not quite as it is actually 16.7%). But that isn't true when looking for the odds over time of eventually hitting one.

Uhh... I believe you :P Feel free to give more examples and stuff but for now I won't go through the trouble figuring it out since I'm in the middle of a test week, or however you call it, if you even have it... Basically I've got two tests every day this week so I'm kind of busy :)

I only asked it because it has been bugging me for some time, I don't want new riddles to bug me for now so I'm not planning on opening this thread the rest of this week, just so you don't wait for answers from me or anything, feel free to hijack the thread though :P

Draug, actually it is. If you roll the dice infinitely there is a 0.167% chance you will ever roll a 6.

troll? you're saying almost no chance you will ever roll a 6 :) jeez I can't concentrate on my homework :P

oh wait, get what you mean SYnapse but you're wrong, Draugnar is right in his last post...

Back to homework.

The chance is 0.167% ad infinitum. There is a large mathematical chance that you will never roll a six.

Please don't tell me I'm wrong when I know more about this than you steephie22. Common sense does not apply in mathematics.

SY. I believe you meant never, not ever, in your post before.

calculations, then? sounds like bullshit to me... Not sure what you're saying in your last message but the one before that is definitely wrong. In one roll the chance to get a six is already 16.7%, that only goes up with more rolls.

@synapse: the chance of never rolling a six gets arbitrarily close to zero as you roll the die more and more times.

It seems like what you are trying to say is that each time you roll a die, you have a 1/6=~16.7% chance of getting a six. Note that .167% is very different than .167 or 16.7%

I'm referring to this: "Draug, actually it is. If you roll the dice infinitely there is a 0.167% chance you will ever roll a 6."

Turns out you've sent another message meanwhile :)

Sorry yeb, you're correct I meant 16.67%

The chance to roll a six does not go up when you roll the dice a second time steephie.

OK, that clears that part up, but, as I see it, you claimed that you have the same amount of chance to throw a six when you're throwing one die as when you're throwing 10 million dice... That's not true of course...

steephie, each roll constitutes an independent event and the odds of rolling a six do not increase as you take more rolls. A roll of the dice is not conditional probability, in other words. This is the same principle on which a roulette table operates. The table shows you the last sequence of numbers and colors to make you think that a certain color or number is due, but in reality each spin has the exact same chance of hitting red/black/green despite the spins that came before it.

Let's say we roll the dice 3 times.
Chance of getting a 6 is 3 out of 18 possible results which is still 1 in 6.