### Brain Teasers

# Shooting Star

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

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?

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?

### Hint

What is the probability that they don't see a shooting star over the course of an hour? Ten minutes?### Answer

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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