Assuming that each marble can be picked with equal probability, we notice that there is a total of
[tex] 4+2+5+1+7 = 19 [/tex]
marbles, of which 2 are red.
So, the probability of picking a red marble is
[tex] \dfrac{2}{19} [/tex]
In fact, as in any other case of (finite) equidistribution, we used the formula
[tex] P(\text{event}) = \dfrac{\text{number of favourable cases}}{\text{number of all possible cases}} [/tex]
