Geometric Probability

1. A point on $\overline{SU}$ is chosen at random. What is the probability it will also lie on $\overline{SR}$ ?

$\dfrac{1}{7}$

$\dfrac{1}{2}$

$\dfrac{9}{16}$

$\dfrac{7}{16}$

Question 1 of 10

2. A point on the line segment below is chosen at random. What is the probability of it being between 14 and 18?

$\dfrac{4}{5}$

$16$

$\dfrac{2}{5}$

$\dfrac{7}{16}$

Question 2 of 10

3. A point on the line segment below is chosen at random, what is the probability of it being between 25 and 30?

$\dfrac{1}{5}$

$\dfrac{2}{3}$

$\dfrac{1}{3}$

$\dfrac{5}{6}$

Question 3 of 10

4. A point on the line segment is chosen at random, what is the probability of it being between 58 and 63?

$\dfrac{1}{6}$

$\dfrac{5}{12}$

$\dfrac{5}{8}$

$\dfrac{3}{4}$

Question 4 of 10

5. An archer is trying to hit the target shown below. The radius of the bullseye is 5 inches. The width of the outer rings are both 5 inches. What is the probability that the arrow will hit the bullseye?

$\dfrac{2}{3}$

$\dfrac{1}{9}$

$\dfrac{1}{3}$

$\dfrac{1}{4}$

Question 5 of 10

6. A triangle is inscribed in a square. Point F in the square is selected at random. What is the probability that F lies in the shaded region?

$\dfrac{2}{5}$

$\dfrac{1}{4}$

$\dfrac{1}{2}$

$\dfrac{2}{3}$

Question 6 of 10

7. A rectangle is inscribed in a circle with the measurements below. What is the probability that a random point will lie in the rectangle. Leave your answer in terms of $\pi$ .

$\dfrac{48}{25} \pi$

$\dfrac{56}{25} \pi$

$\dfrac{3}{5} \pi$

$\dfrac{4}{5} \pi$

Question 7 of 10

8. A circle is inscribed in a square with the following measurements. What is the probability that a random point will lie in the circle? Leave your answers in terms of $\pi$ if necessary.