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Lessons 1: Planets

In this lesson, members of a group of people each pick their favorite planet (we have included Pluto in our list). How many people do you think will have to be in the group so that the chance of two people picking the same planet is 50%?

Doing the science

  1. Load the Pick-A-Pair Sim. If the opening screen is not the Planets problem, click on the Planets link at the top of the screen.
  2. Move the cursor to the right of the zero (0) in the "How many in the group" area.
  3. Press the "Backspace" key to remove the zero and enter the number of people you would like to have in your group (a number between 1 and 40).
  4. Press the "Start" button and examine the results.
  5. Press the "Next" button for a new trial – once again, examine the results.
  6. Continue pressing the "Next" button to see the results of each new trial.
  7. After the ninth trial the simulation will operate automatically and record the data for 50 trials. Record your data in Table 1.
  8. If the percentage of trials with a match was less than 50% then increase the number of group members and try again. Similarly, if the percentage of trials with a match was greater than 50%, decrease the number of group members.
  9. Your goal is to find a group size (N) which results in a greater than (or equal to) 50% chance of a match and a group size (N-1) results in a less than 50% chance.

Table 1.

# in group

# of trials

50

50

50

50

50

50

50

50

50

Trials with a match

Percentage

Do You Understand?

  1. What was the minimum number of people needed for a 50% chance of two people picking the same planet?