When there are few data, we often fall back on personal probability. There had been just 24 space shuttle launches, all successful, before the Challenger disaster in January 1986. The shuttle program management thought the chances of such a failure were only 1 in 100,000.

(a) Suppose 1 in 100,000 is a correct estimate of the chance of such a failure. If a shuttle was launched every day, about how many failures would one expect in 300 years?

(b) Give some reasons why such an estimate is likely to be too optimistic.