The number of outcomes in the sample space equals the number of marbles:

$\displaystyle{4}+{5}+{6}={15}\usepackage{cmbright}\Huge\$

The number of outcomes for the event of pulling a red marble from the bag is 4. So $\displaystyle\frac{{4}}{{15}}\usepackage{cmbright}\Huge\$ is the probability of pulling a red marble from the bag.