Chapter 4, Problem 4.176ACB

NASA and rare planet transits. A “planet transit” is a rare celestial event in which a planet appears to cross in front of its star as seen from Earth. The National Aeronautics and Space Administration (NASA) launched its Kepler mission, designed to discover new planets in the Milky Way by detecting extrasolar planet transits. After 1 year of the mission in which 3,000 stars were monitored, NASA announced that five planet transits had been detected (NASA, American Astronomical Society, January 4, 201 0). Assume that the number of planet transits discovered for every 3,000 stars follows a Poisson distribution with λ = 5. What is the probability that, in the next 3,000 stars monitored by the Kepler mission, more than 10 planet transits will be seen?