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# Help Me!

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So, just please don't give the answer if I'm wrong, I wanna learn, not cheat. So basically, I have this problem:

A fair coin is flipped 7 times. What is the probability that at least 5 consecutive flips come up heads?​

I'm pretty sure this calls for some casework (which I hate). Basically, what I did was list out all the possible ways this favorable outcome could happen, and I got:

THHHHHT

HHHHHTT

TTHHHHH

THHHHHH

HHHHHHT

HHHHHHH

as the possible cases. But the thing is, these cases have the exact same probability of happening. In fact, any coin flip sequence has the same probability as another. So, is this answer just $$\frac{6}{2^7}$$? I have 6 favorable outcomes and 2x2x2x2x2x2x2 possible ways to roll.

Is this right? There is a different answer here: https://web2.0calc.com/questions/a-fair-coin-is-flipped-7-times-what-is-the-probability-that-at-least-5-of-the-flips-come-up-heads but idk if it's right.

Aug 5, 2020

#1
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There is a difference between your question and the one answered by heureka at : https://web2.0calc.com/questions/a-fair-coin-is-flipped-7-times-what-is-the-probability-that-at-least-5-of-the-flips-come-up-heads; namely you are asking for 5 consecutive heads, whereas the other questions just asked for 5 heads (not necessarily consecutive)..

For your case, have you ignored HHHHHTH and HTHHHHH ?

Aug 5, 2020
edited by Alan  Aug 5, 2020
#2
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Ah

I feel so dum

And I think that they are the only 2 missing, right?

THHHHHT

HHHHHTT

HHHHHTH

TTHHHHH

HTHHHHH

THHHHHH

HHHHHHT

HHHHHHH

Yes, i think that's it.

So... $$\frac{8}{2^7}=\frac{8}{128}=\frac{1}{16}$$

THANQ

Inspirational  Aug 5, 2020