I assume you mean the bag contains 4 black marbles.
There are 16 marbles total and we assume that outcomes are equally likely. That is, we assume that any particular marble is just as likely to be chosen as any other. Then, since there are 16 marbles total, the probability of selecting any particular marble is $1/16$.
In general, if outcomes are equally likely, then to find the probability of an event $A$, compute
$$\text { size of }A\over\text{total number of outcomes}.$$
In the above "size of $A$" is the number of outcomes that make up $A$.
For $A$ being the event "a black or red marble was chosen", the size is $7$, (one of the 4 black or one of the 3 red were chosen). So, the probability that a black or red marble was chosen is $ 7/16$.
If $A$ is the event the event "a yellow or green marble is chosen", the size of $A$ is 9, and the corresponding probability is $9/16$.
Obviously, the second quantity is the greater one (which could have been seen without doing any arithmetic, since the size of "yellow or green" is larger than the size of "black or red").