## The Spinning Wheel

Materials: Margarine tub spinner or graphing calculator
or a table of random table of numbers.

Imagine a spinner with three sectors, all the same size, marked
1, 2, and 3. The experiment consists of spinning the spinner
three times and recording the numbers as they occur (e.g. 123)
We want to determine the proportion of times that at least one
digit occurs in its correct position. For example, in the numbers
123, all of the digits are in their proper position, but the number
331, none are. For this activity, use a spinner, a table
of random digits or your TI-83.

### Hypothesis

1. Guess the proportion of times at least one digit will occur
in its proper place.

### Experiment

2. To use you calculator to randomly generate the three-digit
number, enter the command randInt(1,3,3).
Continue to press ENTER to generate more three-digit numbers.
Use a tally mark to record the results in a table like the one
below. Do at least 20 trials and then calculate the relative
frequency for the event "at least one digit in the correct
position."

To use a random number table, select a row,
and discarding digits 4 to 9 and 0, record digits in the 1 to
3 range in groups of three.

Click **here **for a Fathom demonstration of this experiment

3. Now combine your results with those
of your classmates to obtain as many trials as possible (at least
100 randomly generated three-digits; 200 would be better.)

Count the number of times at least one digit
occurred in its correct position, and calculate the proportion.

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