Group Activity Cards

 Use groups of 2. Materials: Notebook paper, two-colored counters, cup, masking tape, marker Plink-Plunk

A popular game consists of dropping circular chips into one of 6 openings on an enclosed game board. The chip bounces off of metal studs in the board until it settles into one of the 5 collection slots at the bottom. In this activity, you will conduct a simulation to explore the probability that a chip will land in the number 3 slot if it is dropped from the second opening on the left.

It is equally likely that a chip will go to the right or to the left of a stud as it falls down the game board. Similarly, it is equally likely that a two-colored counter will land on one color or the other. So you can toss a two-colored counter to simulate outcomes. Follow these steps.

Step 1 Use masking tape to mark 9 counters with the numbers 1 through 9, one on each counter. Then place these counters into the cup and toss them on your desk.
Step 2 If a counter lands red side up, this indicates a fall to the left of a stud. If a counter lands yellow side up, this indicates a fall to the right of a stud. Line the counters up in order, from 1 to 9.
Step 3 Record the path of a falling chip in a table like the one shown. Trace this path on the game board, starting at the second opening on the left, and record the number of the slot where the chip eventually lands. Keep in mind that the direction of a fall can be controlled by the edge of the game board. If an outcome indicates a fall to the left, but the only possible move is to the right, ignore that outcome, move to the right, and go on to the next outcome.

 Outcomes 1 2 3 4 5 6 7 8 9 Slot Trial 1 L L R L L L R L R 1 Trial 2 R R L L R R R R R 4 Trial 3 L R L L L R R R R 3 Trial 4 R L L R R R L L R 2

Step 4 Repeat Steps 1-3 until you have 50 trials.

Find the experimental probability that a chip will land in slot 3 if it starts at the second opening from the left. Suppose the object of the game is to have your chip land in slot 3. Based on your experimental probability, is starting your chip at the second opening a good strategy for winning the game? Explain.

Compare your experimental probability with that of other groups in your class. Are your results similar? Why or why not?

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