A similar thing thing happened in 1962, during the Cuban missile crisis.[0]
The math is sobering. Even if we assume 'only' a 1% chance per year, that implies a 63% probability per century.
The math is sobering. Even if we assume 'only' a 1% chance per year, that implies a 63% probability per century.
I'm not sure I'm following the math here?
Putting it in terms of "probability per century" is intended for forward-looking projection, not backwards.
So it's
P(bomb exploding in a century) = 1 - P(bomb not exploding in a century) = 1 - (P(bomb not exploding in a year)) ^ 100 = 1 - (1 - P(bomb exploding in a year)) ^ 100
Why is it not something simpler, like P(bomb exploding in a year) ^ 100 ?
That would be "bomb exploding EVERY year (= this year AND next year AND ...)".
What we actually want is "bomb exploding this year OR bomb exploding next year OR bomb exploding this year and next year OR bomb exploding in two years OR ...". But that's too complicated, so we use the trick with 1 - P(bomb not exploding in a century).