### Home > CCG > Chapter 7 > Lesson 7.2.4 > Problem7-88

7-88.

Kendrick is frantic. He remembers that several years ago he buried his Amazing Electron Ring in his little sister’s sandbox, but he cannot remember where. A few minutes ago he heard that someone is willing to pay $\1000$ for it. He has his shovel and is ready to dig.

1. The sandbox is rectangular, measuring $4$ feet by $5$ feet, as shown at right. If Kendrick only has time to search in the $2$ foot-square shaded region, what is the probability that he will find the ring?

Compare the area Kendrick has time to search to the area of the entire sandbox.

$\frac{4}{20}=\frac{1}{5}$

2. What is the probability that he will not find the ring? Explain how you found your answer.

The sum of the probabilities of finding the ring and not finding the ring equal to $1$.

3. Kendrick decides instead to dig in the square region shaded at right. Does this improve his chances for finding the ring? Why or why not?

Compare the size of this shaded region to the shaded region on part (a).