# Linked Questions

26answers
5k views

### Applications of complex numbers to solve non-complex problems

Recently I asked a question regarding the diophantine equation $x^2+y^2=z^n$ for $x, y, z, n \in \mathbb{N}$, which to my surprise was answered with the help complex numbers. I find it fascinating ...
5answers
17k views

### Probability for the length of the longest run in $n$ Bernoulli trials

Suppose a biased coin (probability of head being $p$) was flipped $n$ times. I would like to find the probability that the length of the longest run of heads, say $\ell_n$, exceeds a given number $m$, ...
3answers
13k views

0answers
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### is it possible to find out how many times coin will return head in n-sequence?

I would like to ask: If we throw a coin 1000 times, expected result is we will get 500 heads from it, correct? Now, is it possible to calculate how many times (max value) head will be selected in ...
0answers
26 views

### Does the number of the same side appearing in a row converge to a finite number? Fair coin toss.

Toss a fair coin N times. Does the number of the same side appearing in a row converge to a finite number? If yes, what is it in terms of N? Are confidence intervals needed? Thank you!