What caused the crash of TWA Flight 800 in 1996? Physics professors Hailey and Helfand of Columbia University believe there is a reasonable possibility that a meteor hit Flight 800.

They reason as follows. On a given day, 3000 meteors of a size large enough to destroy an airplane hit the earth's atmosphere.

Approximately 50,000 flights per day, averaging two hours in length, have been flown from 1950 to 1996. This means that at any given point in time, planes in flight cover approximately two-billionths of the world's atmosphere.

Determine the probability that at least one plane in the last 47 years has been downed by a meteor.

(Hint: Use the Poisson approximation to the binomial. This approximation says that if n is large and p is small, a binomial distribution with parameters n and p is approximately Poisson distributed with λ = np.)