2D Geometric Probability
How Often Does The Coin Hit The Red Circle?
The figure above shows the base (of radius 11 ) of a cylindrical bucket. There is a red circle of radius 4 centered at the center of the base. If Barry throws a coin of radius 1 into this bucket, what is the probability that the coin will land in contact with the perimeter of the red circle?
Give this problem a try before jumping in for the solution!
Solution
Notice that the coin will be in contact with the red circle if the center of the coin lands in the shaded area shown below.
The shaded region is the inner area of a circle of radius 5 subtracted by the inner area of a circle of radius 3. Given that the coin’s radius is 1, the coin’s centre cannot land farther than 10 units from the centre of the bucket’s base.
The probability is therefore
Well done!
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Barry 🍩