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Bowl for a Car

During a special promotion, a charity has set up a bowling lane in a mall. One blindfolded contestant will roll a ball down a lane at a single pin. If the ball touches the pin, the contestant wins a new car. The diameter of the bowling ball is 21.8 cm. The diameter of the pin is 10.2 cm. The lane created is 101.6 cm. Side rails prevent the ball from leaving the lane.

  • Determine the possible outcomes in this situation.
  • The pin is placed in the middle of the lane. what is the probability that the ball will strike the pin?
  • The charity has purchased an insurance policy that will pay for the car if the contestant wins. To reduce the probability that a car is won, the insurance company suggests placing the pin on the right-handed edge of the lane. Is the company correct?

 


Hint: Draw a picture...where could the ball go in order to miss the pin? Think in terms of fractions of total width of the lane.

 


Solution Commentary: No solution provided...sorry folks!

This problem generated so much discussion and contrary solutions during a recent series of secondary math workshops that it was necessary to share it with a larger audience. Thanks Ron!