# A dice roll game probability question!?

I have a question and it would be great if someone could provide the answer along with a helpful explanation as to how they got the answer.

There is a dice game where you play with a 10 sided dice (pentagonal trapezohedron dice). The only way to lose this game is if you roll either a 1, 2, 5 or 7, for 5 consecutive rolls in a row! So if on roll number one you roll a 3 you already won the game. However if your first roll if you roll a 1, then second roll a 7, then third roll a 5, then fourth roll a 2, then fifth and final roll a 5 then you finally lose.

My question is this, what is the probability of losing? What is the probability you would either roll a 1, 2, 5 or 7 for 5 rolls in a row. I understand each event is an independent event, however there is a set number of rolls to do so, 5.

Thanks so much to whoever answers!

Be safe,

Bret.

### 1 Answer

- ?Lv 65 months agoFavourite answer
There are 4 numbers you want to avoid. The probability of getting one of those numbers on a given roll is 4/10 = 0.4. The probability of getting one of those 5 times in a row is 0.4^5 = 0.01024. (This is where the independence of the rolls comes in--you can just multiply 0.4 by itself 5 times.)

So you have about a 99% chance of winning, and slightly more than 1% chance of losing.