I am stuck on computing probability problem that goes as follows:
I am rolling a 6 sided die 5 times in total. What is the probability that I roll at least one 3, but no 1 or 2 at all (= probability of rolling at least 3 but at least one dice has to be 3).
Examples that satisfy my condition:
Examples that do not satisfy my condition:
- 45445 (satisfy at least 3, but does not satisfy at least one dice has to be 3)
- 32653 (does not satisfy at least 3, satisfy one dice has to be 3)
The part of rolling at least one 3, as far as I know, should be opposite event to no 3 at all: $$1 - \left(\frac56\right)^5 = 0.5981.$$
I am stuck on the second part.