Roy Cleveland Sullivan was an American park ranger in Shenandoah National Park in Virginia. He holds the Guinness Book of World Record for most lightning strikes on a human. Seven lightning strikes were documented but he was probably struck even more times. In many of these strikes, his hair caught on fire, so he carried a water bottle to dowse himself. Sullivan believed the clouds actually followed him during a storm and had lightning rods installed on his four-poster bed. What is the probability of being hit by lightning 7 times in a lifetime?
According to the National Weather Service, the probability of being struck by lightning once in a lifetime is approximately 1/15300. The probability of one person being struck by lightning 7 times is p = (1/15300)7 = 5.1 x 10-30. During the lifetime of Mr. Sullivan, the world population (say n) was between 2 and 3 billion. So, we can ask whether, in a world with a population of n = 2.5 x 109, is it unusual to be struck by lightning seven times? Since p is very small and the world population n is a large number, we can use the Poisson distribution to estimate the probability that someone would be hit seven times. The Poisson parameter is m = np = 1.28 x 10-20. The probability that at least one person in the world is struck by lightning seven times is 1-e-m ~ m = 1.28 x 10-20. This means that Sullivan’s being struck by lightning was an extremely low probability event.