Conditional probability and the intersection Assuming you have an unfair die where the probabiity of rolling a certain number is defined as follows: 
$$
\begin{array}\\ 
\text{Die Face} & 1 &2&3&4&5&6\\
\hline\\
\text{Probability} & .05 &.2 & .1 &.2 &.3 & .15
\end{array} 
$$
Find the probability that we roll an even number followed by an odd number. 
I would think this is a conditional probability question, however, in the solutions it simply said that rolling an odd number first and rolling an even number second are two events $A$ and $B$ respectively, and then by independence said: $P(A)=.05+.1+.3=.45$ and $P(B)=.2+.2+.15=.55$ and $P(A\cap B)=P(A)P(B)=(.45)(.55)=.248$. When I worked this out first I thought this would be done by conditional probability. Why would my reasoning be wrong here? And why can we solve this problem like this?

It’s not a problem in conditional probability: it simply asks for the probability of a specific sequence of independent events, which is of course the product of their individual probabilities, just as the text’s answer has it.
It’s no different in principle from the following question: given a fair coin, what is the probability of tossing a head followed by a tail?
