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%.
Today's brain teaser courtesy of Braingle.com.