How to find the probability of getting a continuous series for a certain number of trials?

Question

Mathematics

Find the probability that among 420 coin tosses there can be at least one series of 7 continuous heads.
The probability of falling heads is 50%.

Answer 1

Remembering the university course, maybe it's worth looking at the sequence of tests according to the Bernoulli scheme?

Answer 2

0.5 x 0.5 x 0.5 x 0.5 x 0.5 x 0.5 x 0.5 =
0.7%

Answer 3

goandkill answered correctly, but not completely correct. 0.7% is the probability of a streak if we have only one attempt per streak in total. But attempts to make a series of eagles are 414. Not 420 for the reason that if we get tails on the 414th attempt, we already lose the opportunity to make a series of heads, since there are only 6 throws left. So, the correct answer is 0.7% x 414 = 289.8%