Question 116997: This is one question amounst a few more that I have to answer within a essay regarding the Law of Large numbers, is there any way you can help me explain this one please.
Explain your answer to the following question: Is it true that if I get tails 3 times in a row that my chances of getting heads on my next toss is greater than 50%?
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!
Flipping coins
If you want to know the  of a coin landing  , heads is the favorable outcome. There is    for a coin to land heads, so the  of the    .
The sample space consists of the total number of ways that a coin can land. Since a coin can  land   or  –  - the sample space is made up of    and the denominator of the probability fraction is  .
Thus the probability of a coin landing heads is  , which is the same as saying that a coin lands heads  % of the time.
What is the probability of the coin landing tails? We can do the same analysis as for the coin landing heads, finding a probability of , or, knowing that if a coin doesn't land heads it has to land tails, and understanding that   of the  MUST be equal to , subtract:
the probability of a coin landing tails must be  .
In this case,   (a 1/2 chance of landing either heads or tails) remain  ; NO MATTER HOW MANY TIMES you flip a coin,  time the coin is EQUALLY likely to fall or .
Even if your coin has fallen heads times    , the chance that the next toss will fall tails is still  %.
So, if you get tails  times in a row your chances of getting heads on your next toss is NOT greater than %.
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