A student has 60% chance of passing in English and 54% chance of passing in both English and Mathematics. What is the percentage probability that he will fail in Mathematics ?

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Q: 141 (IAS/1995)
A student has 60% chance of passing in English and 54% chance of passing in both English and Mathematics. What is the percentage probability that he will fail in Mathematics ?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,9,14,5,7,2,9

keywords: 

{'percentage probability': [0, 1, 0, 0], 'mathematics': [0, 1, 0, 0], 'english': [1, 0, 0, 0]}

The student has a 60% chance of passing in English. This means there is a 40% chance of failing. Since we are advised that there is a 54% chance of passing in both English and Mathematics, this probability is also the chance of passing in English and not failing in maths. It means the pupil will satisfy these two criteria at the same time. Therefore, the possibility of the student failing in Maths when they pass in English can be found by subtracting the 54% joint probability from the 60% probability of passing in English. This leaves a 6% chance that the student passes in English but fails in maths. However, since the student has a 40% chance of failing in English, we can infer that they likewise have a 4% chance of failing in Mathematics as well (40-36=4%). Hence, the correct answer is option 3, which is 4%.

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