Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let square of size $10\times 10$ is divided into two $5\times10$ rectangles: A and B. Toss a coin with radius $1$ into the square. What's the probability that the coin is completely in A?

I have no idea about this problem. I even don't know what's the sample space. Can anyone guide me how I can go on?

share|cite|improve this question
In some problems in geometric probability, there can be quite different answers depending on one's hoice of sample space. Hard to know what is natural here. Maybe centre of square uniform on the inner $8\times 8$ square. – André Nicolas Nov 6 '12 at 2:12

I'm going to assume that by tossing a coin into the square, they want the coin completely in the square. Consider where the center of the penny could land and still be within rectangle A. It can't land within a radius length of a boundary without some part of the coin overhanging it, so the area that the center of the coin can land in such that the coin is completely in A would be $3\times8$, or 24.

So, to finish the problem, I'd try calculating the area the center of the coin could land and still remain in the square. The probability would be the ratio of the 2 areas.

share|cite|improve this answer
oops. Was thinking diameter 1 for some reason. Corrected. – Mike Nov 6 '12 at 12:00

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.