MaryJae
One in 100 Chance It Will Flood Each Year
RECEIVED Tue., Oct. 19, 2004
My dear Editor,
Andrew Rooke points out correctly that the 100-year flood plain is misnamed, because it doesn't mean that a flood will happen every 100 years, but rather that there's a one in 100 chance it will flood in one year ("Postmarks," Oct. 1). Many readers were probably puzzled because that looks like the same thing. But it's not.
You'd think that if there's a one in 100 chance in one year, then after 100 years there's a 100 in 100 chance. That's the same thing as a 100% chance. But logically we know this can't be true – it's certainly possible that it might not flood during a 100-year period. So this tells us that we can't simply add the probabilities together.
So now that we know what doesn't work, let's see what does work. If you flip a coin once the chances of getting heads are 50%, or one in two. If you flip it twice the chances of getting two heads are 50% for the first flip and 50% for the second flip. So that's 50% x 50% = 25%, or one in four. So to figure the probability of a repeated event we simply multiply the probabilities.
To solve our flood problem, we'll take the probability of the event not happening in 100 years and then subtract that from 100% (the probability that it definitely would have happened). The probability of there being no flood in one year is 99/100. After 100 years it's 99/100 x 99/100 x 99/100 etc., 100 times. That gives us 36.6%. So if there's a 36.6% chance of a flood not happening in 100 years, then there's a 63.4% chance that it will flood in 100 years.
This assumes it can't flood twice in one year, but let's not get picky.
Andrew Rooke points out correctly that the 100-year flood plain is misnamed, because it doesn't mean that a flood will happen every 100 years, but rather that there's a one in 100 chance it will flood in one year ("Postmarks," Oct. 1). Many readers were probably puzzled because that looks like the same thing. But it's not.
You'd think that if there's a one in 100 chance in one year, then after 100 years there's a 100 in 100 chance. That's the same thing as a 100% chance. But logically we know this can't be true – it's certainly possible that it might not flood during a 100-year period. So this tells us that we can't simply add the probabilities together.
So now that we know what doesn't work, let's see what does work. If you flip a coin once the chances of getting heads are 50%, or one in two. If you flip it twice the chances of getting two heads are 50% for the first flip and 50% for the second flip. So that's 50% x 50% = 25%, or one in four. So to figure the probability of a repeated event we simply multiply the probabilities.
To solve our flood problem, we'll take the probability of the event not happening in 100 years and then subtract that from 100% (the probability that it definitely would have happened). The probability of there being no flood in one year is 99/100. After 100 years it's 99/100 x 99/100 x 99/100 etc., 100 times. That gives us 36.6%. So if there's a 36.6% chance of a flood not happening in 100 years, then there's a 63.4% chance that it will flood in 100 years.
This assumes it can't flood twice in one year, but let's not get picky.
Michael Bluejay
college dropout
college dropout
