7th Grade Math Question of the Day

1. $\frac{2}{9}$
2. $\frac{1}{4}$
3. $\frac{1}{3}$ (correct answer)
4. $\frac{4}{9}$

Explanation: When you encounter probability problems involving geometric shapes, remember that probability equals the favorable area divided by the total area. Here, you need to find what fraction of the entire target is occupied by the middle ring. First, calculate the area of each circle using the formula $A = \pi r^2$. The innermost circle (radius 2) has area $\pi(2^2) = 4\pi$. The middle circle (radius 4) has area $\pi(4^2) = 16\pi$. The outermost circle (radius 6) has area $\pi(6^2) = 36\pi$. The middle ring is the area between the circles with radii 2 and 4 inches. To find this, subtract the smaller circle's area from the larger one: $16\pi - 4\pi = 12\pi$. The probability is the middle ring's area divided by the total target area: $\frac{12\pi}{36\pi} = \frac{12}{36} = \frac{1}{3}$. Looking at the wrong answers: Choice A ($\frac{2}{9}$) likely comes from incorrectly using the ratio of radii rather than areas, or making an arithmetic error. Choice B ($\frac{1}{4}$) might result from comparing the middle ring to just the middle circle instead of the entire target. Choice D ($\frac{4}{9}$) could come from finding the outer ring's probability instead of the middle ring. Study tip: In geometric probability problems, always work with areas (or lengths for 1D problems), never just the given measurements. The $\pi$ terms will cancel out, so focus on getting the area calculations right.