Probability 13th Birthday Occurs On Friday the $13$th Alright math wizards, this is probably a fairly simple one... I'm interested in knowing what the probability is that a person has their $13$th birthday on Friday the $13$th (in any month). I'm especially interested in the formula used to solve this.
Here's my best guess. There is (roughly) a $1$ in $30$ chance that a person is born on the $13$th day of any given month. There is a $1$ in $7$ chance that a person's $13$th birthday occurs on a Friday. Multiplying these two probabilities $(7 \times 30)$ yields roughly a $1$ in $210$ chance that a person's $13$th birthday occurrs on Friday the $13$th.
 A: $\frac{1}{210}\approx 0.00476190$
There is a slight error in your calculation due to your assuming "thirty days on average" for a month, where in fact it is closer to $\frac{365.24}{12}\approx 30.437$ days per month on average.
Using this to correct your solution, we have have a seemingly more accurate approximation as $\frac{1}{30.437\cdot 7} \approx 0.0046935$
The solution that you suggested is close to accurate.  However, due to the nature of our calendar, friday the thirteenth is slightly more probable than one might expect.  Read this page for more.  The thirteenth of the month is more likely to be a friday than any other day of the week (by a fraction of a percentage, but still).
Our calendar system repeats once every 400 years (or 146097 days).  Out of the 146097 days in the gregorian calendar, exactly 688 of them are friday the thirteenths.  We may rephrase the question from "thirteenth birthday is friday the thirteenth" to "is born on friday the thirteenth" (ignoring chance of death as a child).
Assuming each day of our calendar is equally likely then, the probability should be $\frac{688}{146097}\approx 0.0047092$.
