Linda, 31, is a philosophy major who went to Berkeley. She is deeply concerned with social justice and discrimination and participated in antinuclear demonstrations. Which alternative is more likely: a) She is a bank teller; or b) She is a bank teller and an activist in the feminist movement?Discussion below the fold.The authors note that 85% of those asked this question made the "boneheaded error in basic logic" of choosing the second option. Why is it boneheaded? Because the second option is a subset of the first option, and therefore cannot be more likely.
Why not? Let's say I have a bag with a hundred marbles in it, 35 red and 65 black. Of the red marbles, some have a green spot on them and others do not. Is it more likely that you will pull out a red marble, or a red marble with a green spot? Logically, even if 34 of the 35 red marbles have green spots, it will be less likely because the green-spot-reds are a subset of the reds. Even if all of the reds have green spots, it cannot be more likely that you will pull out a green-spot-red than a red.
The process that is fooling the test-takers is that they are considering the question as two separate cases: Is it more likely that she is a bank teller, or a feminist activist? There's no special reason to believe a philosophy major (let alone one concerned with 'social justice and discrimination') will become a bank teller; so it seems far more likely that she is an activist. Thus, the option that includes the higher-probability choice seems more probable overall -- even though, in fact, it can't be.