The GSS has a variable, ODDS1, which represents the question:

Now, think about this situation. A doctor tells a couple that their genetic makeup means that they've got one in four chances of having a child with an inherited illness. Does this mean that if their first child has the illness, the next three will not have the illness?

The obvious answer is that each child is an independent "trial," and so has a 1 out of 4 chance. Only 10% of the respondents answered incorrectly. Below are the frequencies against some variables of interest (whites only, sample sizes 1500-2500).

The variables were EVOLVED, GOD (atheist to confident theist left to right), DEGREE (lowest to highest education attained, left to right), POLVIEWS (extremely liberal to extremely conservative, left to right), SEX and WORDSUM. Running quick Logit through the GSS interface WORDSUM, EVOLVED and SEX had statistically significant coefficients (at p = 0.05 for EVOLVED and p = 0.01 for the other two).

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The WORDSUM data looks particularly visually striking. The data for WORDSUM=0,WORDSUM=1 and WORDSUM=2 is very interesting. I'm almost inclined to wonder if the very low vocab of these people made them have trouble understanding the question.

In the cases where the the coefficients were not statistically significant there appear to be clear correlations just from eyeballing. Further study is clearly needed.

I'd also be interested in how people answered a slightly different question. Consider the question: "A doctor tells a couple that their genetic makeup means that they've got one in four chances of having a child with an inherited illness. They first child they have has inherits the illness. Is the chance that the next child will have the illness still one in four?" I suspect that the percentage who could answer this correctly would be much lower.

Then why is the gambler's fallacy so common? (ie. The notion that a heads is "due" after flipping ten tails in a row?)

Deadpost, that was sort of the point of my comment. I suspect that many people will think that the heads is more or less due but won't think that it is guaranteed.

OK, I am almost scared to ask how many living breathing adults actually didn't know any of the words on WORDSUM. The graph shows percentages not body count (head count would give them too much credit). The smallest number of folks that could possibly be represented by such percentages would be three, and mercifully one even knew the correct answer. Let's hope that number really is three out of the sample size of 1500-2500. In their defense, at least they have the excuse of being either ignorant or dumb.

What is up with all the college grads who got it wrong? !

I mean, this is an elementary school topic, four crying out loud!

deadpost,

Maybe people who would still succumb to the gambler's fallacy would still get this right because it's such a strong statement. E.g. they might know that the next three will not get the illness, but they might still think it's less likely that they will. Maybe they understand that it's still a matter of chance, but not that that chance is unchanged.

sg,

I have met a lot of people who came to college with what seemed like solid math backgrounds (differential equations and the like) who had trouble with probability. It surprised me too.

Those percentages for WORDSUM=0 looked suspicious to me too. I checked and found that there were actually four (among the 1546 whites who also replied to ODDS1) respondents with a WORDSUM of 0, but there's some kind of bug in the software as the percentage is wrong. Only one of those four got the question right.

The percentages are much closer to correct for those with a larger sample, but still off by a little. My first guess was that it was simply a counting error, but that doesn't seem to work with the other columns. I don't know what's going on there.