There is a very small risk, which I estimate is conservatively about as dangerous as driving in a car for 15 miles.
About 15 people per year are shocked by lightning while using water in their house in the United States (the country for which I have data).
"Ron Holle, a former meteorologist with the National Oceanic and Atmospheric Administration who tracks lightning injuries, estimates that 10 to 20 people in the US are shocked annually while bathing, using taps or handling appliances during storms."
About 12 per cent of people struck by lightning are killed. Of 240 people struck by lightning in the US in 2012, 28 were killed. Let's assume that rate is the same for water-related strikes. So the average number of US citizens killed by lightning during water use is about 12 per cent. So, out of a population of 312 million in the US, there were 1.8 deaths, or a rate of 0.5 deaths per 100 million people per year.
There were about 40 'thunderstorm days' in an average US state in 2010. This sounds high if you live in California or the north-east, but the south and midwest have a lot more thunderstorms which pull the average up.
So, assuming there is one thunderstorm per thunderstorm day, the death rate is 0.013 deaths per 100 million people per thunderstorm. This is if you act normally.
Normal people wouldn't usually shower during a thunderstorm, because a) the storm usually isn't happening at the exact time when they want to shower, even on a 'thunderstorm day', and b) they avoid showering during thunderstorms. In order to figure out how much you increase your risk by showering during a thunderstorm, we need to estimate both of these rates.
(a) to me seems reasonably estimated as the chance that a daily 20 minute period with a shower or other contact with water will overlap with a one-hour thunderstorm, my guess at the average length of a storm. This is roughly 1/24.
(b) is trickier – how much less likely are normal people to shower during a thunderstorm? I think this is somewhere between 10x and 100x. Lots of people have heard that it is dangerous to shower during a thunderstorm and will avoid it. But some storms start while people are showering, others might not be aware that a storm is happening, and others will just risk it. I'll say 50x to be conservative.
Putting all this together, you have about 50*24*0.013/(100 million) = 16 deaths per 100 million for someone who takes an extra shower during a thunderstorm.
The risk of death by driving a car was 1.1 deaths per 100 million miles travelled in 2011. So, if you believe the assumptions above, the risk of death from taking a shower during a thunderstorm is about equivalent to 15 miles driven.
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