A bag contains 3 red marbles worth 2 points each if drawn, and 7 blue marbles worth 0 points. If one marble is drawn at random, what is…

Expected value weights each outcome by its probability. A red marble is drawn with probability $\frac{3}{10}$ and is worth $2$ points, and a blue marble is drawn with probability $\frac{7}{10}$ and is worth $0$. So $E=\frac{3}{10}(2)+\frac{7}{10}(0)=0.6$, choice A. Choice D ($2.0$) is the value of a red marble, ignoring how unlikely it is. Choice B ($0.7$) is the probability of drawing blue. Choice C ($1.0$) is the average of the two point values, $\frac{2+0}{2}$, which wrongly treats red and blue as equally likely. The expected value must be less than $2$ because most marbles are worth nothing.