In a coaching batch, 60% of the students sat the mathematics test and 45% sat both the mathematics test and the reasoning test. If a student picked at random is known to have sat the mathematics test, what is the probability that the student also sat the reasoning test?

Being told the student sat mathematics narrows the batch to that 60%, and the question asks what share of THAT group also sat reasoning: 0.45/0.60 = 0.75 = 3/4. In 100 students, 60 sat mathematics and 45 of those 60 also sat reasoning. Trap 9/20 = 0.45 quotes the joint figure and forgets to rescale to the smaller group. Trap $27/100=0.60\times 0.45$ multiplies where it should divide. Trap 3/20 = 0.60 − 0.45 subtracts instead — that 15% is the maths-only share.