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Ok im taking a video game desing class. I have to answer the question if i flip a coin 10 time what is the probability of it landing on heads 4 times in a row. I do not know the equation for this problem. I know what it would be if it was 4 times over all but not 4 times in a row. Can someone please help me?

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  • $\begingroup$ Do you count TTHHHHHTTT as containing 4 heads in a row, or do you require exactly 4 heads in a row? $\endgroup$ – Parcly Taxel Oct 17 '16 at 2:59
  • $\begingroup$ Im going to say the count because the question simple just states as i write it other then it talks about it being used for a video game. $\endgroup$ – Teaformylov Oct 17 '16 at 3:04
  • $\begingroup$ Huh? So you mean the sequence I showed does contain 4 heads in a row? $\endgroup$ – Parcly Taxel Oct 17 '16 at 3:05
  • $\begingroup$ Sure i mean it meets the rules of the question so why would it not count? And it is a possible out come that has 4 heads in a row. The question word for word says if you are playong a game where you flip a coint 10 time and inorder to win you have to have it land on heads 4 times in a row what are the chance of this happening. $\endgroup$ – Teaformylov Oct 17 '16 at 3:13
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When you see a problem regarding probability like this one, you have to break it down into two parts.

1) the specified outcome, which will be the numerator of your final answer. 2) the total number of outcomes, which will be the denominator.

The specified outcome is the number of ways you can have four tails in a row in the 10 flips. This is found by calculating how many distinct groups of 4 consecutive flips there are within these 10 lines. If you do a little counting, you can see that there are 7 groups. Therefore, for 10 flips, there are 7 ways you can arrive at your desired result.

Now, just count the number of total outcomes, which is 2^10 because you have two outcomes for each flip and 10 flips in total.

Therefore, 7/1024 is your answer.

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  • $\begingroup$ Ok that makes since. Idk if you can help me with this because i have to show my work. So that would requir the equition to be writen out so that would be write this though? So would it be (2^10) but how would i do the other part of the problem. It makes since the whole it can only happen before flip 7 by just simple counting but i dont understand how to write it. $\endgroup$ – Teaformylov Oct 17 '16 at 3:45
  • $\begingroup$ Note that this answer only applies if the sequence is to have exactly 4 heads in a row and no other heads in the entire sequence. $\endgroup$ – cocoahomology Oct 17 '16 at 8:09

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