In a hostel of 200 students, 40% travel by the campus bus, 60% subscribe to the mess, and 25% both travel by the bus and subscribe to the mess. A student is picked at random from those who do NOT travel by the campus bus. What is the probability that this student subscribes to the mess?

Work in head counts out of 200. Bus users = 40% of 200 = 80; mess subscribers = 60% of 200 = 120; both = 25% of 200 = 50. Mess subscribers who do NOT use the bus = 120 − 50 = 70, and students who do not use the bus = 200 − 80 = 120. The condition restricts the group to those 120, so the probability is 70/120 = 7/12. Trap 5/8 = 50/80 conditions on the wrong group — that is the mess share among BUS users. Trap 3/5 = 120/200 quotes the overall mess share and ignores the condition entirely. Trap 7/20 = 70/200 keeps the right numerator but divides by the whole hostel instead of by the non-bus group.