Homework Questions
Simulations
Unit 6
Experimental Estimates

As the number of trials in an experiment
increases, the relative frequency of an
outcome approaches the probability of
the outcome.
numberoftrialswithoutcomeinE
P( E ) 
n
Example 1 (review)

An experiment consists of throwing a
dart at a target. Suppose the experiment
is repeated 200 times, with the following
results:
yellow 43, red 86, blue 71
 Write the probability
distribution for the experiment

Probability Simulations
In order to estimate probability using the
experimental approach, a large number
of trials is needed.
 Instead of actually carrying out the
experiments, computer simulators are
used…aka your calculator!

Random Number Generator

On your calc:
Math
 Prob
 5: RandInt(

Example 2




Use your calc to create Outcome
a probability distribution
for the experiment of
0 heads
tossing 3 coins and
counting the number of
1 heads
heads.
Assign 0=heads, 1-tails
2 heads
RandInt(0, 1, 3)
Repeat 10 times
3 heads
Frequency Prob.
Experimental v. Theoretical
Experimental Probabilities are what
happens when you carry out the
experiment.
 Theoretical probabilities are used when
outcome are equally likely.


Rolling a dice = 1/6 chance each time
Example 3

Use properties of
probability to write a
theoretical
probability
distribution for the
experiment in #2.
 How do these
compare to #2?
Outcome
0 heads
1 heads
2 heads
3 heads
Options
Prob.
Counting Techniques
A catalog offers chairs in a choice of 2
heights, regular and tall. There are 10
colors available for the finish, and 12
choices of fabric for the seats. The chair
also has 4 different possible designs.
How many different chairs can be
ordered?
Example 5

Each letter of the alphabet is written on a
piece of paper, and three letters are
chosen at random. There are two
important questions to ask:
Is each letter replaced before the next letter
is chosen?
 Does the order of the letters matter in the
result?

With replacement – the number to chose
from stays the same
 Without replacement – the number to
chose from decreases by one each time
 Order important – CAT is different than
ACT
 Any order – CAT, CTA, TAC, TCA, ACT,
and ATC are considered the same

3 letters are chosen…
With
Without
replacement,
replacement,
order important order important
Without
replacement,
any order
Homework

Worksheet (1-25)