a square target is shown. a dart is dropped randomly onto the target. the dart is equally likely to hit any…

a square target is shown. a dart is dropped randomly onto the target. the dart is equally likely to hit any spot on the target. 18 cm 18 cm 3 cm 3 cm *not drawn to scale what is the probability that the dart will hit a spot in the shaded square? a. $\frac{1}{2}$ b. $\frac{1}{6}$ c. $\frac{1}{9}$ d. $\frac{1}{36}$

a square target is shown. a dart is dropped randomly onto the target. the dart is equally likely to hit any spot on the target. 18 cm 18 cm 3 cm 3 cm *not drawn to scale what is the probability that the dart will hit a spot in the shaded square? a. $\frac{1}{2}$ b. $\frac{1}{6}$ c. $\frac{1}{9}$ d. $\frac{1}{36}$

Answer

Explanation:

Step1: Calculate large - square area

The area formula for a square is $A = s^2$, where $s$ is the side - length. For the large square with $s = 18$ cm, $A_{1}=18\times18 = 324$ $cm^{2}$.

Step2: Calculate small - square area

For the small shaded square with $s = 3$ cm, $A_{2}=3\times3=9$ $cm^{2}$.

Step3: Calculate probability

The probability $P$ that the dart hits the shaded square is the ratio of the area of the shaded square to the area of the large square. So $P=\frac{A_{2}}{A_{1}}=\frac{9}{324}=\frac{1}{36}$.

Answer:

D. $\frac{1}{36}$