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## Shooting Star

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 Puzzle ID: #21554 Fun: (2.46) Difficulty: (2.53) Category: Probability Submitted By: tsimkin

Henry and Gretchen plan on sitting outside to look for shooting stars. They know from experience that if they watch for an hour, they will have a 90% chance of seeing a shooting star. It is a chilly night, though, so Gretchen says, "Let's only stay out for 10 minutes."

Henry says, "I was really hoping to see a shooting star tonight. If we are only out for 10 minutes, we will only have a 15% chance."

Gretchen replies, "Not true. We have a better chance than that."

Is Gretchen right? If so, what is the probability that they see a shooting star?

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 aardvark Mar 17, 2005 a good refresher on my probability course, thanks! CHUCKLZ Mar 17, 2005 ok...Had the right answer but I did not figure it out that way...good job lilbutt Mar 18, 2005 Me no like math. (user deleted) Mar 25, 2005 me no like math live w/ it changegurl May 05, 2005 Bye! nuccha Oct 27, 2005 Hmmm.... really nice work... although i think the distribution should be made known. Just a thought. nuccha Oct 27, 2005 Hmmm.... really nice work... although i think the distribution should be made known. Just a thought. tsimkin Oct 27, 2005 nuccha -- when you say describe the distribution, do you mean say something like, "The arrival of shooting stars can be modeled as a Poisson distribution with a lambda of 2.302585 for one hour"? This could certainly be said (and indeed backed into, which is how I just came up with the number), but I thought the statement that they had a 90% chance of seeing at least one in an hour sounded cleaner than that. hidentreasure Nov 10, 2005 He is right you know Jimbo Feb 27, 2006 Nice puzzle. We call it a binomial distribution which is well defined anyway. tsimkin Feb 27, 2006 The number of shooting stars you see in an hour have a poisson distribution, not a binomial. The two are pretty close when the expected number (lambda in a poisson distribution) is high, but look pretty different (much more highly skewed for a poisson) when lambda is low. jsdodgers Sep 13, 2006 your brain teasers are confusing javaguru Dec 11, 2008 Nice problem. You certainly don't need to describe the distribution other than the assumption that the events are independent and random. The reality with meteor strikes does not quite fit that description, but the problem didn't give enough information to make any other assumption. To tsimkin: Poisson distribution! That would be useful to work out if you wanted to answer a question such as "What is the probability that you'll see x number of meteor strikes within 10 minutes?" (For example, the probability of seeing three meteors in 10 minutes would be ~0.0039.) It seems like overkill for this problem though. opqpop Sep 29, 2010 I've seen this before Thanks for the refresh.