# Calculating the probability of seeing a shooting star within half an hour if we know it for one hour

The probability to see a falling star in the sky over the course of one hour is 0.64.

What is the probability to see it over the course of half an hour?

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An hour is two half hours. If the probability in each half hour is $p$, the probability not to see a falling star in the entire hour is $(1-p)^2=1-0.64=0.36$, so $1-p=0.6$ and $p=0.4$. Note that $0.64$ was chosen such that the square root could be easily drawn with or without taking complements, so you wouldn't have noticed if you hadn't taken complements.

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This assumes that the probabilities of seeing a shooting star in two consecutive half-hours are independent. However, both cloud cover and meteor showers can last many hours, so if one of the half-hours is in a period of increased meteor activity/visibility, chances are that the second one is too. (Of course, this reasoning has the disadvantage that it means the question does not have enough data to answer it). –  Henning Makholm Feb 14 at 17:18
If you think you will either see one and only one falling star in the hour or not, the chance would be $0.32$ as the $0.64$ is equally spread. The other answer assumes there is a constant density of falling stars in time and you might see more than one. This shows how the assumptions change the answer.
Equally spread? Wouldn't that imply that in 1/0.64 hours the probability will become 1, and you are guaranteed to see one? –  janos Feb 14 at 12:28