Can someone tell me what the odds of not rolling a total of 3 on two dice (that is, a combination of 1 and 2 that totals 3) after 80 rolls of the dice? Each die is 6 sided (your typical dice) with 1 through 6 on each side.
I played an electronic game where after 80 rolls, the total of the 2 dice never totaled 3. I thought this was very unusual and that the odds were astronomical of a total 3 not being rolled after 80 rolls of the 2 dice.
However, I inquired of the maker of the electronic game, and this was their customer service’s response to me:
“Not that I happen to be a mathematician, I calculated the corresponding probability: Of the total 36 possible rolls are only 2 that add up to 3. The probability of rolling anything but a 3 is 17/18. (17/18)^80 = 0.010330309
This means that such an event occurs about once every 100 games. I would not call this ‘astronomical’. ;-)”
Is their calculation of the odds correct ... is it really so that you can roll 2 dice 80 times in a row, and a total combination of 3 not be rolled every 100 games?
Thanks for any input ...
The probability of not rolling a total of $3$ is $\displaystyle \frac{17}{18}$, and for $80$ rolls, $\displaystyle \left (\frac{17}{18} \right)^{80}$ is correctly calculated. Good work.