Probability of rolling a 6 before an odd number

Question

A dice is rolled many times. What's the probability of rolling a 6 before an odd number? I'm unsure of where to start with this, please help.

Answer 1

Think of it this way: Throwing a $2$ or a $4$ is meaningless, so ignore those cases. Without them we have only $4$ equally likely events: $\{6,Odd,Odd,Odd\}$. The probability of getting the $6$ first is then seen to be just $\frac 14$

Answer 2

Note that this does exist, because with probability $1$ you will eventually get a $6$ or an odd number. Suppose the first time you get a $6$ or an odd number is on the $n$'th roll. There is one $6$ and there are $3$ odd numbers, so the conditional probability, given that it happens on the $n$'th roll, is $1/4$. And since that is the same for all $n$, the answer is again $1/4$.