The probability of rolling a "1" on a six-sided die is 1/6. When rolling the die six times, the probability of not rolling a "1" at all is (5/6)^6. Consequently, the probability of rolling at least one "1" in six rolls is calculated as 1 - (5/6)^6, which is approximately 0.6651 or 66.51%. This can also be approached as a binomial probability problem.
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No. You correctly intuit that there is a chance of not rolling any "1"'s at all.piercebeatz said:This question has been bothering me for a while. If you roll a 6 sided die 6 times, is there a 1 probability that you with roll the number 1?
The probability of rolling a "1" is 1/6 for the die. Therefore the probability of rolling any other number is 5/6 ... since the rolls are independent, the probability of rolling anything but a 1 all six times is (5/6)^6 ... so the probability of getting at least one "1" in six rolls is 1-(5/6)^6.What is the percent chance that you will roll the number 1? It clearly isn't 100%...
Simon Bridge said:No. You correctly intuit that there is a chance of not rolling any "1"'s at all.The probability of rolling a "1" is 1/6 for the die. Therefore the probability of rolling any other number is 5/6 ... since the rolls are independent, the probability of rolling anything but a 1 all six times is (5/6)^6 ... so the probability of getting at least one "1" in six rolls is 1-(5/6)^6.
That's the shortcut - you can also set it up as a binomial probability problem.