Anybody know the actual mathematical odds of experiencing a hurricane and an earthquake in the same week?

Not really, but I can take a pass at it. For simplicity, I'll assume we're talking about an earthquake of magnitude 5 or more (since quakes below that magnitude are often not that noticeable). According to the USGS, there are an average of 1469 earthquakes of magnitude 5+ per year, globally. We'll call it 1500 to make the math easy.

According to the University of Colorado's NCAR, there have been an average of 8 hurricanes per year in the last decade or so, a number that has been rising. Hurricanes are seasonal, with the official season stretching for 6 months (26 weeks), though hurricanes can arrive out of season. Hurricanes can remain at hurricane strength for a matter of hours, or can persist for as long as 31 days, so we'll assume a 2 week window.

The probability of one or more hurricanes existing during any given 2 week stretch of hurricane season is about 45% (this takes into account the likelihood of two hurricanes existing simultaneously). During that 2 week period, you'd expect an average of 56 earthquakes of magnitude 5 or more, meaning that it's essentially guaranteed that such an earthquake will strike somewhere on earth during the duration of a hurricane.

Calculating the odds of an earthquake and a hurricane striking the same place gets much trickier, because the odds of a given spot experiencing an earthquake and the odds of that same spot experiencing a hurricane are vary from place to place. In a normal year, Ft. Myers, FL, has a 16% chance of getting hit by a hurricane, while New York has about a 4.4% chance. The New York area has experienced 7 damaging earthquakes in the last 300 years, annual probability of 2.3% (0.045% per week).

Redoing the math, that works out to a probability of a hurricane and an earthquake occurring in the same week in the New York area (during hurricane season) of 0.00015%, odds of about 1:1,500,000.

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Your calculation would apply to next week, but the chances this week are 1 in 1.

Yet, it happened.

Too bad they don't name earthquakes. This could be much more interesting.

There's a Schrodinger's Hurriquake joke in here somewhere...

but the chances this week are 1 in 1.

And they could be next week as well.

There are limits to what probability can tell you and, as this shows, coming up with a valid calculation of probability can be impossible. Situations in real life can become too complex to look at with mathematics or science and then you're left with just trying to exercise judgement on other bases. Though the widespread faith that it is possible or even wise to try is one of the great investigated articles of faith of the last two hundred fifty years.

If you start with global earthquakes, you should also count global tropical cyclones, not just the North American ones ("hurricanes").

I've never experienced an earthquake and a hurricane in one week. However, 1959 brought an interesting two months:

On August 3, I was dumped out of bed by an earthquake of moderate strength that did minor, but noticeable damage throughout the area.

On September 29, a hurricane made landfall just south of us, crossing us with winds of 120 miles an hour and causing considerable damage. I remember watching an unusually tall pine tree in the front yard twisting in the dirt until it broke free, then rising straight up into the air before crashing back to the ground.

On October 1, while we were still navigating downed power lines, cooking on outdoor grills, and getting water from neighbors with wells, a huge Standard Oil (Exxon)storage tank nearby caught fire and burned for several days. I remember the huge clouds of black smoke and the fears that the fire would spread to other tanks and/or trigger a massive explosion.

People were in such shock that some were adding up the disasters of earth, wind, and fire to get the total "end of the world."