A bag is full of 20 bananas and no other fruit. Rajeev draws a fruit from the bag. What is the probability that he will draw a banana?

An embarrassing 30 per cent of the country's engineers cannot solve a problem as simple as the one above, a study has found. Their ineptitude, however, is not limited to just sums of probability.

It's worse as over one-third engineers do not possess mathematical skills needed in day-to-day life for doing simple transactions, counting and arranging. In other words, they have a weak understanding of concepts as elementary as decimals, powers, operations, ratio, fractions and the ability to apply these concepts to real-world problems.

Raising serious questions about the quality of education in schools and engineering institute, the study states, "These skills are required in all engineering and analytics jobs in the knowledge-based industry. For instance, an engineer who cannot multiply/divide decimal numbers (the total being an alarming 42 per cent) would face difficulty in doing basic engineering calculations."

The study, released by Aspiring Minds, is based on the results of more than 55,000 students from over 250 engineering institutes who took AMCAT test. The engineers had graduated in 2011. Aspiring Minds, started by MIT alumnus Varun Aggarwal and IIT-Delhi graduate Himanshu Aggarwal in 2008, this standardised tests, whose test scores are used by top companies to recruit freshers. Almost 30,000 students take this test every month.

The report also raises concern over the language skills of the fresh engineering graduates. Given the importance accorded to a candidates fluency in English during the interview process, the report states that a sizeable chunk of the engineers are far from impressing the recruiters they don't have the "English comprehension skills to understand engineering school curriculum".

"Twenty five to 35 per cent engineers cannot comprehend English usage even in day-to-day conversations. Since engineering education is in English, this is a key concern for colleges, as such a lack inhibits students from grasping concepts in other subject areas as well," the report states. To illustrate the weak vocabulary, the study states that more than half the number of students did not understand words such as absurd, generic, cease and adamant, among others.

It's probably not surprising why less than 25 per cent of the enginneers joining the workforce every year are seen as unemployable by the industry.

There are, however, people who are sceptical of the findings. According to S.S. Mantha, chairman, AICTE, the report should not be believed entirely as the sample size of students is small.

"There are 1.5 million students at the entry-level in engineering students. Even if we assume that one million graduate as engineers, then a sample size of 55,000 students is too small to make such sweeping comments on the mathematical and language ability of all the students," Mantha said.