CPM Homework Help : CCG Problem 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.

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?
Hint (a):
Compare the area Kendrick has time to search to the area of the entire sandbox.
Answer (a):
$\frac{4}{20}=\frac{1}{5}$
What is the probability that he will not find the ring? Explain how you found your answer.
Hint (b):
The sum of the probabilities of finding the ring and not finding the ring equal to $1$ .
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?
Hint (c):
Compare the size of this shaded region to the shaded region on part (a).