What is the probability of seeing a shooting star?

The probability of anything is always conditional. Never forget that. As others point out, the probability of seeing a shooting star depends on many things that can make that probability either very low (near 0) or very high (near 1). read more

So the probability of not seeing a shooting star in a half hour is $e^{-\lambda}=\sqrt{0.09}=0.3$. The probability of seeing at least one is therefore $0.7$. Remark: The probability of seeing at least one shooting star in half an hour cannot be $0.455$. read more

The probability of seeing a shooting star, given that you happen to glance up at the sky at random for 5 seconds one night while waiting for a train at the station at the center of a big city, is very nearly 0. read more

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. read more