Geometric probability question

[kazuchan]

A dog is running around in a fenced-off rectangular field with dimensions of 40ft by 50ft. If the position of the dog is uniformly random throughout the field, what is the probability that the dog is 10 feet or more away from the fence at any given time?

In know that since the dog is uniformly random throughout the field that the probability that the dog will be in any region of the field is equal to the ratio of the area of that region to the area of the entire field.

So the area of the entire field is 50x40=2000 ft
and the area of the marked off field is (50-10)x(40-10)=1200 ft
Now, I find the ratio (1200/2000)=3/5=.6 which gives me a probability of the dog being 10 feet away from the fence 60% of the time.

When I went to check my answer, it said that the dog was away 30% of the time. How could this be?

Thank you for your help!

 

[Office_Shredder]

If you're ten feet away from the top.
AND you're ten feet away from the bottom

That's twenty less feet of room you have to move in

 

[kazuchan]

got it! thanks for pointing that out!