When there are few data, we often fall back on personal probability. There had been just 24 space shuttle launches, all successf
ul, before the Challenger disaster in January 1986. The shuttle program management thought the chances of such a failure were only 1 in 100,000. 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? [a] (Round to the nearest integer.)
There are about 110,000 days in 300 years, so the expected number of failures is about 10/11 ≈ 1.
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This assumes the launch conditions are identical for each of the launches, or that whatever variation there might be has no effect on the probability. These are bad assumptions.
