Question: A survey was conducted to test relative aptitudes in quantitative and logical reasoning of MBA applicants. It is perceived (prior to the survey) that 80 percent of MBA applicants are extremely good in logical reasoning, while only 20 percent are extremely good in quantitative aptitude. Further, it is believed that those with strong quantitative knowledge are also sound in data interpretation, with conditional probability as high as 0.87. However, some MBA applicants who are extremely good in logical reasoning can be also good in data interpretation, with conditional probability 0.15. An applicant surveyed is found to be strong in data interpretation. The probability that the applicant is also strong in quantitative aptitude is
Suppose 100 MBA applicants were surveyed.
80 of them are good in logical reasoning and 20 are good in quantitative aptitude.
0.87 × 20 ≈ 17 are good in quantitative aptitude and in data interpretation as well.
0.15 × 80 = 12 are good in logical reasoning and in data interpretation as well.
Thus, there are 17 + 12 = 29 MBA applicants those are strong in data interpretation.
Of the 29 MBA applicants 17 are strong in quantitative aptitude.
Hence, option (b).