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

 Mar 3, 2020
 #1
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Probability  is

 

P( 5 flips come up  heads)  + P( 6 flips  come up heads)  + P (7 flips  come up  heads)  =

 

C(7,5) (1/2)^5 (1/2)^2  +  C(7,6)(1/2)^6 (1/2)  + (1/2)^7   =  29  /  128

 

cool cool cool

 Mar 3, 2020
 #2
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Nice work CPhill. But, there is something wrong with it. I don't know what it is though. Thanks for the help. If you dont answer this, it is fine as you have already dedicated a lot of your time to this problem.

Guest Mar 3, 2020
 #3
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CPhill: Look at your own answer to the same question here:

 

https://web2.0calc.com/questions/need-help-please_30

 Mar 3, 2020
 #4
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At least 5 consecutive heads =8 / 2^7 =1 / 16
HHHHHHH, HHHHHHT,HHHHHTH, HHHHHTT,
HTHHHHH, THHHHHH, THHHHHT, TTHHHHH

 Mar 4, 2020

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