Objectives

  • Develop intuition about sample spaces, events, combinations, and permutations.

Instructions: Birds and Coins

Scenario

You are conducting research on a species of small bird, the brown creeper, in Oregon. Your research site consists of 6 forest plots, each 1 hectare in area. The 6 plots are all nearly identical in their characteristics.

You know from past surveys that on a given day, you usually find brown creepers in about half of your survey plots. You conduct your daily survey and find brown creepers in 2 of the 6 plots.

Since youโ€™re studying discrete distributions and probability theory in class, you wonder how likely you are to have observed exactly two presences, out of six plots given that birds are typically present in about half of the plots.

You happen to have some coins laying around, so you decide to use them to help.

Question 1

  • How could you define an event in your sampling scheme? Explain your reasoning.

Question 2

  • What is the sample space of your bird sampling scheme?

Question 3

  • You observed two presences and 4 absences in your daily survey. One possible spatial arrangement of these presences/absences is:

How many ways are there to arrange the two presences in your grid of six plots? Explain how you found your answer.

Question 4

  • Given that the probability of observing a brown creeper presence in a given forest plot is about 50%, do you think that observing exactly 2 presences is an unusual event? Explain your reasoning. HINT: The coins might help with this question.

Instructions: Acorns

Consider the acorn questions from the reading questions. As a group, use the acorns at your table to answer the following questions regarding the acorns of the three species.

Question 5

Consider the scenario in which you pick up two acorns at the same time in one hand without looking.

  • Enumerate the events in this sample space.
  • Are these events combinations, or permutations?
  • Make sure you explain your reasoning.

Question 6

Consider the scenario in which you pick up one acorn, place it in your left pocket, walk a short distance, then pick up a second acorn and place it in your right pocket.

  • Enumerate the possible events in this sample space.
  • Are these events combinations, or permutations?
  • Make sure you explain your reasoning.

Report

Compile your answers into a document and upload it to Moodle.