Very simple probability question

[pierce15]

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? What is the percent chance that you will roll the number 1? It clearly isn't 100%...

 

[Simon Bridge]

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?

No. You correctly intuit that there is a chance of not rolling any "1"'s at all.

What is the percent chance that you will roll the number 1? It clearly isn't 100%...

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.

 

[pierce15]

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.

Thanks a lot!