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I Probability of getting 3 heads or more in 20 coin flips

  1. Jun 19, 2016 #1
    hey folks,

    My question is how to find probability of getting 3 CONSECUTIVE heads or more in 20 coin flips, what are the odds

    I have an approach which I need to verify and please clarify in case of missing points.

    No. of possible outcomes = 2 ^ 20

    first I assume that first 3 outcomes are heads , all other 17 combinations of coins are to be counted, so there are 2 ^ 17 .
    then I assume first outcome is tail, and 2nd,3rd,4th outcomes are heads, all other 16 combinations of coins are to be counted , so there are 2^16
    then I assume first outcome AND second outcome both are tail, and 3rd,4th,5th outcomes are heads , other 15 combinations are 2^15
    then I assume first outcome , second outcome AND third outcome all are tail, and 4th,5th,6th outcomes are heads , other 14 combinations are 2^14

    and so on until
    1st to 17th outcome are all tail , and 18th,19th,20th are heads, possibility is 2^0 which is 1

    so the answer is 2^17 + 2^16 + 2^15 + ...... 2^0 which gives 262143 , with a probability of 0.25

    are there any misleading overlapping cases?

    and please check R software or matlab or others to get the exact answer
    Last edited: Jun 19, 2016
  2. jcsd
  3. Jun 19, 2016 #2


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    You can go to wolframalpha.com and check it yourself.
  4. Jun 19, 2016 #3


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    You omitted all cases where early flips were heads, but not 3 consecutive.
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