# Probability of Winning the Carnival Game of Tossing a Coin Into a Table

**Problem**

In a common carnival game, a player tosses a penny from a distance of about 5 feet onto the surface of a table ruled in 1-inch squares. If the penny (3/4 inch in diameter) falls entirely inside a square, the player receives 5 cents but does not get his penny back; otherwise he loses his penny. If the penny lands on the table, what is his chance to win?

A. 5/16 | C. 9/256 |

B. 1/16 | D. 3/128 |

**Answer Key**

[ B ]

**Solution**

$x = 1 – 2(3/8) = 1/4 ~ \text{inch}$

$P = \dfrac{(1/4)^2}{1^2} = 1/16$ ← Answer: [ B ]

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