NASA and statistics

On NPR this morning I heard NASA administrator Michael Griffin explaining why he thought it was ok to dismiss safety concerns raised by two of his managers regarding the upcoming shuttle launch. He said that since they'd had 114 flights and never lost a vehicle due to the particular problem area identified by the managers, he found it "unreasonable to think it was likely" that they would lose one in the future. There are so many things wrong with that reasoning it's hard to know where to begin. Couldn't his (2x) predecessor have said almost exactly the same thing about any foam falling off the external tank prior to the final flight of Columbia? Has he ever heard of Poisson statistics? As my thesis advisor said while on the Columbia Accident Investigation Board (Times of London, April 30, 2005): "[T]he risk of a serious failure is between 1 and 2 per cent a launch, or between 24 and 43 per cent over the 28 missions still planned"
Griffin's no dummy - what he really wants to say (but can't do so explicitly because it would be so impolitic) is that he considers the risks acceptable, given that the alternative is to declare the shuttle program done because they can't retroactively fix this design flaw. What a mess.