This problem is related to our discussion in class of the Gambler\'s Fallacy. As

Question

This problem is related to our discussion in class of the Gambler's Fallacy. As in our discussion, suppose that you start flipping a fair coin, and the first 10 flips happen to be tails, but on the flips after the first 10, the number of heads equals the number of tails. What will be the relative frequency of heads after 1 million total flips? What will be the relative frequency of heads after 10 trillion total flips? In our classroom discussion, Adam argued the following (this is the Gambler's Fallacy): Since the coin is fair, the definition of probability requires that, in the long run, the relative frequency of heads must be approximately 1/2 To achieve this, because of the initial sequence of 10 tails, there must be some extra heads later on, to compensate for the extra tails during the earliest flips. Explain how your computations in parts a and b of this problem help show that Adam is mistaken.

Explanation / Answer

answer
the total one million in which 10 are done already and remaining have 50% chance so
relative frequency is 499995
because every event is independent of each other

b
relative frequency of heads after 10trilion total flips is

=4999999999995
c
the every event is independent of each other so that the probability will be predicted for remaining events and the known events do not affect the future probability of events

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