Imagine yourself at a conference center, where there are two groups meeting in adjoining rooms, one a group of lawyers and the other a group of engineers. In fact, the room with lawyers contains 30 lawyers and the room with engineers contains 70 engineers. Someone named Jack is attending a meeting in one of these two rooms. Here is what we are told about Jack: he is a 45-year-old man who is married and has four children.
He is generally conservative, careful, and ambitious. He shows no interest in political and social issues and spends most of his free time on his many hobbies, which include home carpentry, sailing, and mathematical puzzles. What probability would you assign to Jack being an engineer?