## 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.