A bag contains 5 red marbles, 4 blue marbles, and 3 green marbles. If one marble is drawn at random, what is the probability that it is…

The bag holds $5+4+3=12$ marbles, and $4+3=7$ are not red. So $P(\text{not red})=\frac{7}{12}$, choice B. Equivalently, $1-\frac{5}{12}=\frac{7}{12}$. Choice A ($\frac{5}{12}$) is the probability of drawing red, the opposite of what is asked. Choice C ($\frac{5}{7}$) compares red marbles to non-red marbles, which is an odds ratio rather than a probability out of all 12. Choice D ($\frac{4}{5}$) compares blue marbles to red marbles and has nothing to do with the total number in the bag. A probability always uses the whole sample space in the denominator.