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

Quiz: Common Maxima and Minima Problems in Calculus

Problems in this quiz involves common variable relationship of maximum and minimum values. All problems in this quiz can be solved without the use of differentiation provided you memorize the variable relationship for maximum and minimum values of each case.

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Solution are provided at the end of the quiz for you to see how to solve the problem without differentiation.

Important: You can only take this quiz once.

Random Steps of a Drunk Man: Probability of Escaping the Cliff

Problem
From where he stands, one step toward the cliff would send the drunken man over the edge. He takes random steps, either toward or away from the cliff. At any step his probability of taking a step away is 2/3, of a step toward the cliff 1/3. What is his chance of escaping the cliff?

A.   2/27 C.   4/27
B.   107/243 D.   1/2

 

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