Consider the following scenario of Tversky and Kahneman: Let A be the event that before the end of next year, Peter will have installed a burglar alarm system in his home. Let B denote the event that Peter's home will be burglarized before the end of next year. Intuitively, which do you think is bigger, P (A|B) or P (A|Bᶜ)? Explain your answer. Intuitively, which do you think is bigger, P (B|A) or P (B|Aᶜ)? Explain your answer. Show that for any events A and B (with probabilities not equal to 0 or 1), P (A|B) > P (A|Bᶜ) is equivalent to P (B|A) > P (B|Aᶜ)?
