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**Unformatted text preview: **1. Two main differences between Classical and Empirical probabilities.
First difference
Classical probability is a theoretical computation.
Empirical probability is computed based on experiment or observation.
Second difference
Empirical probability makes no assumptions when it comes to possible outcomes.
Classical probability assumes the occurrence of any possible event within the
sample space is the same as any other.
2.
1
1
T
2
H
3
H
4
T
5
H
6
T
7
H
8
T
9
H
10 T
2
H
H
T
T
H
T
H
T
T
H
3
H
T
T
T
T
T
T
T
T
H
4
H
T
H
T
H
T
T
T
T
T
5
H
T
H
T
H
T
T
H
H
H
6
H
H
H
H
T
H
T
H
H
H
7
T
T
H
H
T
H
T
T
T
H
8
T
T
T
H
H
T
T
H
T
H
9
T
T
H
T
H
H
H
T
T
T
10
H
T
T
H
H
T
H
H
H
H
11
T
H
T
T
T
T
T
H
H
T
12
H
H
H
T
H
T
H
H
H
T
13
T
H
T
H
H
H
H
H
T
H
14
T
H
H
H
H
H
H
H
T
H
15
T
H
H
H
T
T
H
H
T
H
Observed probability of tossing a head: 8heads/16coins = ½
Observed probability of tossing a tail: 8tails/16coins = ½
The same number of heads and tails occurred in four trials: 3, 5, 8 and 10
What kind of probability are you using in this bag of coins experiment?
Empirical probability
Compute the average number of heads from the ten trials.
8 + 9 + 10 + 7 + 10 + 6 + 9 + 10 + 7 + 10 = 86
Heads/10
86/10 = 8.6
Change this to the average probability of tossing heads.
8.6/16 = 0.5375 or 8.6/16*100 = 53.75%
16
H
H
H
T
T
H
H
H
H
T
Did anything surprising or unexpected happen in your result for this
experiment?
No, I expected more heads than tails that is usually how these experiments turn out.
3. write the sample space for the outcomes of tossing three coins using H for
heads and T for tails
Possible outcomes:
T, T, T
T, T, H
T, H, T
T, H, H
H, T, T
H, T, H
H, H, T
H, H, H
What is the probability for each of the outcomes?
1/8
Which kind of probability are we using here?
Classical probability
How come we do not need to have three actual coins to compute the probabilities
for these outcomes?
No coins are needed because we are assuming that each possible outcome is the same.
...

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