Top positive review
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on November 19, 2009
I am revising my review of this book due to the seriousness of one particular error.
On page 126, the author, Deborah Rumsey, addresses "The Famous Birthday Problem." Basically, the problem asks, "Given n people in a group, what is the probability of at least two of them sharing a birthday?"
This problem and its correct solution are well known and can be found in numerous authoritative texts such as William Feller's "Probability Theory and Its Applications" and on the Internet as well.
At first blush, Rumsey's different from the traditional approach to this problem seemed clever to me. However, upon closer examination, her method turns out to be flawed.
For example, if there were four people in the group, the correct calculation for the probability that at least two of the four people share a birthday is:
1 - (365/365)(364/365)(363/365)(362/365)
According to Rumsey's method, however, the corresponding probability would be:
1 - (364/365)(364/365)(364/365)(364/365)(364/365)(364/365)
Rumsey's "solution" is not mathematically equivalent to the first (correct) solution, although, fortuitously, the calculated results are nearly the same (0.0163559 versus 0.0163262). This difference reveals a subtle error in the logic of Rumsey's approach to the problem.
I'm rating this book with a single star because I feel that an error of logic in a book that purports to teach probability is not acceptable. I enjoyed reading Probability For Dummies, but I am disappointed that an otherwise well written, entertaining, and useful book has been stained by a fundamental error in reasoning.
Other errors in the book are:
On page 9, both the definition and example of the term "odds" are incorrect. "Odds" is not the ratio of the denominator to the numerator of a probability, but rather the ratio of the probability of success for a given event to the probability of failure of that event. If the probability of a horse winning a race is 50%, the odds of the horse winning is 1 to 1, not 2 to 1 as the book states.
On page 169, the formula that defines the normal distribution is incorrect. The denominator of the exponent should be "twice sigma", not "sigma".
On page 170, the formula that defines the Z distribution is incorrect. The exponent "minus Z squared" should be "minus Z squared divided by two".