Everyone knows Friday the 13th is regarded as a day of bad luck.
Why does every year have at least one of this bad day?
Source: 2010 ISI B Math UGB

A month has a Friday 13th if and only if it begins on a Sunday.

On a regular (non-leap) year, if January begins on day $k$, $0\leq k\leq 6$ (with $k=0$ being Sunday), then we have that:


January begins on day $k$;
February begins on day $k+3\bmod 7$ (since January has 31 days, and $31\equiv 3\pmod{7}$;
March begins on day $k+3\bmod 7$;
April begins on day $k+6\bmod 7$;
May begins on day $k+8=k+1\bmod 7$ (since April has 30 days, and $30\equiv 2\pmod{7}$);
June begins on day $k+4\bmod 7$;
July begins on day $k+6\bmod 7$;
August begins on day $k+9 = k+2\bmod{7}$;
September begins on day $k+5\bmod 7$;


With these, we already have day $k$, $k+1$, $k+2$, $k+3$, $k+4$, $k+5$, and $k+6$, so at least one of these months will begin on Sunday, guaranteeing at least one Friday 13th.

For Leap years, the analysis is similar, except that:


January begins on day $k$;
February begins on day $k+3$;
March begins on day $k+4$;
April begins on day $k$;
May begins on day $k+2$;
June begins on day $k+5$;
July begins on day $k$;
August begins on day $k+3$;
September begins on day $k+6$;
October begins on day $k+1$. 


So at the latest, you will have a Friday 13th by October.
