Question about the mean

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Question about the mean
Message posted by Tracy Wright on March 23, 2000 at 12:00 AM (ET)

I have a question about the accuracy of a conclusion made by the writer of an article I recently read. Here is an abstract of the pertinent information:

...according to (source's) own figures, the annual in-use failure rate for the 'pill' is as high as 11%. That means that a sexually active 14-yr old girl who faithfully uses the 'pill' has a 44% chance of getting pregnant at least once before she finishes high school.

It is my understanding of probability that (her) chance is 11% period, not 44%. Isn't it inappropriate to add the annual rate for each year to obtain a total rate?

I would appreciate your comments on this.

READERS RESPOND:
(In chronological order. Most recent at the bottom.)

Re: Question about the mean
Message posted by Young Kim on March 24, 2000 at 12:00 AM (ET)

You are right. The annual
estimate of 11% was probably
collected during a one year
study and means a max. probability
of 0.11. If the study was performed
over a 4 year period, the result would
probably be the same. Also, you have to ask
if 0.11 was the max. individual value seen
or was it calculated from confidence interval.
Reads like 0.11 is not an estimate of the mean.

Re: Question about the mean
Message posted by Jack Tomsky on March 28, 2000 at 12:00 AM (ET)

You're right that you can't simply add the probabilities. Otherwise, for ten years, you would end up with a total probability greater than 100%.

If the chance of pregnancy is independent for each of the four years and has the same 0.11 probability, then the probability of at least one pregnacy is 1 - (.89)^4 = 0.373, not 0.44.

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