Math 362 - Lab #1 - Fall 2002
Introduction
to Probability Theory
Lab 1: Experiments, Sample Space, Events
Equipment: a bag containing colored objects of similar
shape. DO NOT LOOK INSIDE THE BAG.
- Experiment:
We call experiment
a process whose outcome is not known in advance with certainty. For instance, perform the
experiment of drawing an object from the bag and recording its color. Indicate
the outcome in the table below and return the object to the bag.
Experiment # | Outcome |
1 | ... |
- Sample space: The possible outcomes of the above experiment are
the different colors, Yellow, Blue, Red, Pink, Black, White, Brown, Green,
Orange of the cubes. The collection of all of these outcomes is called the
sample space of this particular experiment. Draw your own
representation of the sample space below.
- Events: An event is a collection of outcomes, or a
subset of the sample space. In particular, the whole sample space,
as well as the empty set are events. Represent the event corresponding to the outcome
of Experiment #1 above in your sketch of the sample space.
- Estimate the contents of the bag
- Perform 20 experiments, each of which consists in drawing an object from the bag,
recording its color and replacing the object into the bag. Record the outcomes
in the table below:
Experiment # | Outcome | Experiment # | Outcome |
2 | ... | 12 | ... |
3 | ... | 13 | ... |
4 | ... | 14 | ... |
5 | ... | 15 | ... |
6 | ... | 16 | ... |
7 | ... | 17 | ... |
8 | ... | 18 | ... |
9 | ... | 19 | ... |
10 | ... | 20 | ... |
11 | ... | 21 | ... |
- Use the above information to estimate the contents of the bag. You can try to
guess how many objects are in the bag, but do not look yet.
- Look at the contents of the bag. How good was your estimate?
Are you surprised by the contents? Why or why not?
What could you have done to improve your estimation of the contents
of the bag? Would your strategy depend on the number of objects in the bag?
Why or why not?
- Reading Assignment: Sections 1.1 to 1.4
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