A carnival game has a player toss a coin with radius 1cm onto a square table with sides of 17cm. On the table are 9 grey squares, 3cm to a side. To win, a coin must sit entirely within a grey square. The probability of a randomly thrown coin winning is?

1 Answer
MathFact-orials.blogspot.com
May 9, 2017

#P("coin is a winner")=9/289~=3.11%#

Explanation:

Let's think about this question in this way - let's talk about where the centre of the coin can land within 1 square and still be a winner.

The coin has a radius of 1 cm and the grey square is 3 cm to a side. And so the centre of the coin needs to sit 1 cm away from the sides of the square - and that is achieved by having the centre of the circle be within a 1 cm square inside the grey square.

With the coin able to be a winner inside that space, we can see that the area of that space is:

#1 cm xx 1 cm = 1 cm^2#

There are 9 boxes, and so the total area where the coin is a winner is:

#9 xx 1cm^2=9cm^2#

The total area of the table is:

#17cmxx17cm=289cm^2#

Which means that the fraction of the table area where the coin is a winner is:

#9/289~=3.11%#

and that is also the probability:

#P("coin is a winner")=9/289~=3.11%#

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