Lab 5 Probability

Exercise 1: Bernoulli Trials

Find the definition for Bernoulli trail on the internet.
Bernoulli Trial is a theory in statistics that when doing an experiment, one of two outcomes will occur -- success or failure.
Include both the table AND the graph in your lab wikibook.
What is the probability of getting heads or tails?
The probability should be 50% for each since there is a 1 in 2 chance it will be heads and a 1 in 2 chance it will be tails.
From your graph does it appear that there is any bias in the coin?
It seems there was slight bias towards heads than tails, but that sort of thing will happen. We won't see a 50-50 split every time.

Heads: 56
Tails: 44



Heads
Tails
2X
5
7
3X
4
1
4X
3
2
5X
2
1
6X
0
0
7X
0
0
8X
0
0



Exercise 2: Probability With Multiple Outcomes (Dice)

An experiment is...? an process which generates uncertain (but well-defined) outcomes
An outcome is...? the different possibilities of a single trial of an experiment
An event is...? a collection of sample points
Probability is...? a numerical measure of the likelihood that an event will occur

What are all the possible "events" when rolling a dice? any one of the six possible outcomes
What are all the possible "outcomes" when rolling a dice? 1,2,3,4,5,6
In 100 throws of the dice what is the probability that each number (outcomes) will occur? (hint: 100/6) 16.67% chance that any of the 6 will occur
Is there any evidence that the dice was loaded? no because the range was only 6 which is pretty accurate


Outcome
Event
Total # of Events
1
14
100
2
18
100
3
20
100
4
16
100
5
18
100
6
14
100
Exercise 3: Probability of Sums with Multiple Outcomes (Pennies)

Outcome
Event
2 Heads
27
Split (Head &Tail)
48
2 Tails
25
What percentage of the time is the outcome 2 heads? 27%
What percentage of the time is the outcome 2 tails? 25%
What percentage of the time is the outcome 1 head,
1 tail? 48%
Explain how you would calculate the probability for these results.
Because there is a 50-50 chance it will come up as heads, there is half the chance that it will come up as heads in the next outcome which means that we should expect to see the heads/tails combo be approximately double that of the 2heads and 2tails.


EXERCISE 4: PROBABILITY WITH SUMS OF MULTIPLE OUTCOMES (DICE)

What is the probability of each outcome for 1 dice? 16.67% or .1667
What is the probability of each outcome for 2 dice? 8.33% or .833

Put this table in your lab wikibook and calculate the probabilities by multiplying the individual outcomes. Use this to fill in the probability table below.

1 (1/6)
2 (1/6)
3 (1/6)
4 (1/6)
5 (1/6)
6 (1/6)
1 (1/6)
1/36
1/36
1/36
1/36
1/36

2 (1/6)
1/36
1/36
1/36
1/36
1/36

3 (1/6)
1/36
1/36
1/36
1/36
1/36

4 (1/6)
1/36
1/36
1/36
1/36
1/36

5 (1/6)
1/36
1/36
1/36
1/36
1/36

6 (1/6)
1/36
1/36
1/36
1/36
1/36


Dice
2
3
4
5
6
7
8
9
10
11
12
8
10
19
18
18
37
30
24
21
8
7
Frequency
2
3
4
5
6
7
8
9
10
11
12
.08
.10
.19
.18
.18
.37
.30
.24
.21
.08
.07
Because 7 is the median number, there is a much greater chance that it will appear more frequently as well as the numbers close to it.