The conjunction fallacy

For most of us, statistical thinking is one of the most difficult mental tasks. Take this case:
Linda is a young woman, she is single and she majored in philosophy. As a student she participated in the feminist movement and she took part in many demonstrations and other actions. Now she has a job. What is more probable?
(a) Linda is a teacher.
(b) Linda is a teacher and is active in the environmental movement.
Please, first answer the question, before you go on.

What was your answer? I guess you have chosen (b). Probably you have thought something like this: Linda was active in the feminist movement, so she is the type that takes part in social movements. Therefore, it’s not unlikely that later in her live she’ll be an activist as well. Nevertheless, your choice is not correct. We told you that Linda is a teacher and that you had the option to choose between either that Linda is a teacher (a) or that she is a teacher plus something else, namely an environmental activist (b). However, the group of b-people is smaller than the group of a-people, since it consists of people who are (a) plus something else. The group of b-persons is a part of the group of a-persons. Therefore, the chance that Linda is an a-person is bigger than the chance that she is a b-person, who is also an a-person.
Or let me explain it this way, if my explanation is still a little bit obscure to you:
(c) There are many teachers in the world.
(d) Only a part of all teachers in the world are active in the feminist movement.
So (d) is a part of (c), or in other words, the (d) group is smaller than the (c) group. For example (note that the figures are fake, but the idea behind them is not): Suppose that 1% of all people in the world are teachers. Suppose also that 1% of all teachers in the world are active in the environmental movement. So, of every 10,000 people in the world, 100 are teachers, but only one of those 100 teachers is an environmental activist. So, isn’t it by far more likely to meet a teacher, anyway, than one who is in addition active in the environmental movement? So, isn’t it by far more likely that Linda is a teacher, anyway, than that she is a teacher who is moreover active in the environmental movement? Alas, if you didn’t see this you fell prey to the conjunction fallacy. But don’t be ashamed, you were not alone, for statistical thinking is one of the most difficult mental tasks.

Source
Jason Iuliano, “Conjunction”, in: Arp, Robert; Steven Barbone; Michael Bruce (eds.), Bad arguments. 100 of the most important fallacies in Western philosophy. Oxford, etc.: Wiley Blackwell, 2019; pp. 321-3.

See also Daniel Kahneman, Thinking, Fast and Slow. London: Penguin Books, 2012.