Exercise 72 Page 401

Practice makes perfect

a By dividing the area in which Kendrick searches by the total area of the sandbox, we can determine the probability of finding the ring.

Searched area:& 2* 2= 4 ft^2 Total area:& 5* 4= 20 ft^2 Now we can calculate the probability of finding the ring. P(Ring found): 4/20=1/5

b The probability that he does not find the ring is the complement of the probability that he finds the ring.

P(Not finding the ring)=1-P(Ring found) Since we know the probability of finding the ring, we can calculate the probability of not finding the ring.

P(Not finding the ring)=1-P(Ring found)

Substitute

P(Ring found)= 1/5

P(Not finding the ring)=1- 1/5

OneToFrac

Rewrite 1 as 5/5

P(Not finding the ring)=5/5-1/5

SubFrac

Subtract fractions

P(Not finding the ring)=4/5

c Digging in the given area does not change the probability. The probability is still calculated by dividing the area of the searched region with the total area of the sandbox. This ratio has not changed, since the searched region is still a square of 2 by 2 feet.