Lads,
Some background on basic probability theory for ye
When asked the question, what is the probability of a coin toss coming up heads, most people answer without hesitation that it is 50%, 1/2, or 0.5
we get this probability by assuming that the coin is fair, or heads and tails are equally likely
The probability for equally likely outcomes is: Number of outcomes in the event ÷ Total number of possible outcomes
For the coin, number of outcomes to get heads = 1
Total number of possible outcomes = 2
Thus, we get 1/2
However, if you suspect that the coin may not be fair, you can toss the coin a large number of times and count the number of heads
Suppose you flip the coin 100 and get 60 heads, then you know the best estimate to get head is 60/100 = 0.6
This way of looking at probability is called the relative frequency estimate of a probability
The interesting thing with this is that the more you flip the coin, the closer you get to 0.5
Number of coin tosses , # heads, prob to get heads
4, 1, .25
100, 56, .56
1000, 510 .51
10000. 4988, .4988,
Now,
For he last 13 coin tosses to get heads definitely indicates and obvious bias of sorts
I have discovered the following info ( before 2010 superbowl xliii
How many superbowls have there been : 43
How many times NFC won toss: 29
How many times AFC won toss: 14
How many times heads: 22
How many times tails: 21
Therefore
Number of coin tosses, # heads, prob to get heads
43, 22, 0.51
( this proves the coin is adhering to the data presented above whether forced or otherwise)
Number of coin tosses. # NFC, prob to get NFC
43, 29, 0.67
Taking all 43 games as one data set with no regard for the chronology of the distribution the NFC has a 67% chance of winning the toss based on data available
Conclusion:
The coin is biased to NFC 67%
]the bias is forced and adheres to the traditional spread of a 2 choice proability but the outcome is known in advance