Two hundred and fifty shoppers were recorded by age and by how they paid. Under 25: cash 30, card or UPI 70. Aged 25 and over: cash 90, card or UPI 60. One of the 250 shoppers is chosen at random. What is the probability that the shopper is under 25 AND paid cash?

The shopper is picked from the whole survey, so the base is all 250 people and the answer is the single cell 30/250 = 3/25. The other options all condition on something the question never granted: 30/100 = 3/10 is the probability that an under-25 shopper paid cash, 30/120 = 1/4 is the probability that a cash payer is under 25, and 120/250 = 12/25 is the probability of paying cash whatever the age. A joint probability divides by the grand total; a conditional probability divides by a row or a column total, and choosing the wrong denominator is the commonest error with a two-way table.