Make a mathematical prediction

Suppose now that you are watching a fish swim in a perfectly spherical bowl. Imagine that you could figure out where the fish is at any given time. What percent of the time do you think the fish would be closer to the center of the bowl than to the outside glass surface of the bowl?

Collect data to investigate your prediction

One way to check your predictions is to run an experiment. Use the computer simulation provided in this activity page to collect data to support your answers.

This simulation is a bit different than the simulations in the previous activities. It has one fish swimming around randomly in a spherical bowl. The simulation keeps track of the position of the fish at all times and knows whether the fish is closer to the center or to the outside glass surface of the bowl. If you look in the lower right corner of the simulation, you will see a small light called a location indicator. If the fish is closer to the center of the bowl, the location indicator will be yellow. If the fish is closer to the outside the bowl, the location indicator will be red. You can think of yellow indicators in the same way as points that landed in the inner circle for the activities of the previous weeks.

1. Click on the Run button (located under the simulation).

2. While the simulation is running, you will notice that the number in the "Position Measurements" box will increase. When it reaches the number you want to sample, click the "Sample" button (located above the table) to record the data. Notice how the chart indicates the results of your experiment. We suggest that you sample 100, 1000, and 10000 position measurements. Unlike the previous activities, for this one you will not enter the number of positions to be generated. The simulation will generate these positions as long as it is running.

3. Examine the results in the table to answer the activity questions.