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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?

Gretchen is right. The probability that they will see a shooting star is about 32%.

We know that the probability that they don't see a shooting star over the course of an hour is 10%. This is the product of not seeing a shooting star for 6 consecutive 10-minute periods. So if q is the probability of not seeing a shooting star over a 10-minute period, we can say:
0.1 = q^6
q = 0.6813

We know that the probability that they do see a shooting star is just 1 minus the probability that they don't, or 1 - 0.6813, which equals about 32%.

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