Answer:
about 51.77%
Explanation:
The probability you will roll a 2 is the complement of the probability you will not roll a 2.
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p(no 2)
A die has 6 faces, one of which is labeled with 2. The probability of rolling a 2 on any given roll is 1/6, so is 1-1/6 = 5/6 that a 2 will not be rolled. Sequential rolls of the die are presumed to be independent, so the probability of 4 rolls not showing a 2 at any time is ...
p(no 2) = (5/6)^4 = 625/1296
p(2)
The probability that at least one 2 will show up on at least one roll is the complement of this value:
p(some 2) = 1 -625/1296 = 671/1296 ≈ 0.517747
The chance you will roll at least one 2 is about 51.77%.