A library's 240 members are recorded two ways — by membership type and by whether they borrowed an e-book last month. Annual members: 96 borrowed, 54 did not. Monthly members: 36 borrowed, 54 did not. One member is picked at random from among the ANNUAL members only. What is the probability that this member borrowed an e-book last month?

Being told the member is an annual member narrows the group to that row: 96 + 54 = 150 annual members, of whom 96 borrowed. So the probability is 96/150 = 16/25. Trap 8/11 = 96/132 conditions the other way round — it divides by the 132 borrowers and answers 'given that the member borrowed, what is the chance the membership is annual'. The two conditionings are different questions and, as here, give different numbers. Trap 2/5 = 96/240 is the joint probability, dividing by the whole membership instead of by the annual group. Trap 5/8 = 150/240 is merely the share of annual members and never uses the borrowing figures.