One of the most interesting classes I took in grad school (for my MBA) was statistics, even if it was also one of the more difficult courses. I finally learned how to estimate probabilities rather than trying to tally up all the different possible outcomes. I learned what margin of error meant, and standard deviation, and other terms I had seen in reference to various statistics without knowing what they means.

Unfortunately I have trouble remembering much of it now. Just a few days ago I was arguing with my husband over the probability of getting the large straight in Yahtzee if you got 1, 2, 4, 5, and 6 on your first roll. If you re-roll the 1, on the next roll you clearly have a 1 in 6 chance of getting the 3 you need. He argued that since you get two chances, that would mean a 1 in 3 chance of getting the large straight. Since you only use the third roll if the second one failed to yield a 3, and the third roll also gives a 1 in 6 chance of a 3, I say the overall chance of getting the large straight is lower. But I can’t remember how to figure it out.

Of course, it’s not particularly important to be able to calculate the probability exactly. We both know that the probability of his getting the numbers he wants on my handheld Yahtzee is less than for me to get them, because the game likes me better. (Honestly – I’ve had up to four Yahtzees in one game.) But it is just a game, mostly a way to pass the time when there’s not a book handy to read.

There are other areas where understanding statistics is more important. Today’s *Wall Street Journal* has an article on misleading numbers in advertisements, “In Ads, 1 Out of 5 Stats is Bogus.” (Personally, I would have guessed that more like 4 out of 5 stats are bogus.) Just this afternoon, I brought in the mail and found a piece from an auto insurance company. Four out of five times, they claimed, their rates beat the competition. Before throwing it out, I puzzled briefly over the possibilities.

Perhaps they didn’t bother giving a quote when it was clear their rates would be higher, and they only calculated the percentages for the cases where they did give a quote. Perhaps they were only referring to a certain category of customers or type of insurance, where they do have lower rates than the competition. Whatever the case, I am fairly certain they manipulated the numbers somehow to give a misleading impression.

The WSJ article gives other examples, particularly from taste tests. I’ve never paid much attention to numbers given in advertisements because I know they’re misleading, but it’s interesting to find out some of the specific ways that the advertisers do it. The simplest way is not to use a representative sample, so that you can honestly “4 out of 5 prefer X” and people will assume that represents the overall population, while in fact the sample was pulled from people most likely to prefer X.

There are lots of other ways to mislead with statistics, and in more serious ways. Everything related to our economy uses numbers, and they are usually thrown around without an accompanying explanation of where they come from. We are bombarded with numbers related to unemployment, interest rates, debt, deficits, tax rates, inflation, consumer price index, GNP, and so forth.

Then we are expected to make decisions based on those numbers, whether personal decision about how to use our own money, or in elections where we choose who will decide how much to tax us and how to spend the tax money. Even people for whom math was not a dreaded subject may not be inclined to double-check all the statistics quoted in the news.

Fortunately there are some good books out there that can help. One I purchased and found very enjoyable – as well as educational – is *A Mathematician Reads the Newspaper*. It covers not only politics and economics but also science and medicine (and other areas as well). It’s not pleasant to realize how easily so many people are misled by those whose job is supposedly to report the truth. But at least you can learn to recognize those misleading tricks yourself.

As a one-time math major who never studied much statistics, I nevertheless couldn’t resist trying to figure out your dice probabilities. I figure you have 5 chances in 6 of NOT getting a 3. Then 5 out of 6 of not getting a 3 on the third roll either. For a total of 25 chances out of 36 of still not getting a 3, or 11 chances out of 36 of succeeding in the two tries. Does this make sense? I read the book you suggest in your last paragraph, after you told me about it a couple years ago. Since then I have seen newspaper columns by the author (Paulos) a few times. I didn’t appreciate his arrogant attitude toward Bible-believing Christians who don’t accept everything about evolution (I believe that’s what the topic was). But I do enjoy his discussions about probabilities in everyday life.

OK, so I multiply the 5 x 5 and 6 x 6 to get the 25 out of 36? That sounds vaguely familiar. Because for each of the 5 (out of 6) possibilities that I don’t get a 3 on the second roll, there are 5 out of 6 possibilities on the third.

So it comes out to very close to 1 in 3 chances that Jon said, but not for the same reason (he was trying to add, not multiply). I had the number 11 in my head (5 unsuccessful from the second roll leading to 6 chances in the third), but couldn’t decide 11 out of what?