We can model this with a binomial random variable, with sample size n=4 and probability of success p=1/6.
As we have to calculate the probability of getting at least one 2, it is easy to substract from a probability equal to 1 the probability of getting no 2. This can be written as:
[tex]\begin{gathered} P(k\ge1)=1-P(k=0)=1-(1-p)^n \\ P(k\ge1)=1-(1-\frac{1}{6})^4=1-(\frac{5}{6})^4=1-\frac{625}{1296}=\frac{1296-625}{1296}=\frac{671}{1296} \end{gathered}[/tex]The probability of getting at least one 2 in dice rolled 4 times is P=671/1296.
