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

Guest Mar 3, 2020

CPhill · Answer 1 · 2020-03-03T11:08:22

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

Guest · Answer 2 · 2020-03-03T11:36:45

CPhill: Look at your own answer to the same question here:

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

Guest · Answer 3 · 2020-03-04T02:58:22

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