In a management class of 100 students three languages are offered as an additional subject viz. Hindi, English and Kannada. There are 28 students taking Hindi, 26 taking English and 16 taking Kannada. There are 12 students taking both Hindi and English, 4 taking Hindi and Kannada and 6 that are taking English and Kannada. In addition, we know that 2 students are taking all the three languages.
I) If a student is chosen randomly, what is the probability that he/she is not taking any of these three languages?
Ii) If a student is chosen randomly, what is the probability that he/ she is taking exactly one language?

Welcome to this beautiful site, dear Lanair, first!

I am doing the first part of your problem for your persual but you must now attempt the second part here, so that I could be able to learn if you understand the logic behind this problem/sum or not. The policy over AMHD is to guide the students, and not to do their assignments. I hope you will get the clue.

The first part -

Persons who read at least one language = 28 +26+16 - 12 -4 -6 +2 = 50
Persons who read none of languages = 100 - 50 = 50

To find the probability that randomly chosen students reads none of the languages - We know that the probability = successful outcomes / possible outcomes.
= 50 / 100
= 1/2 = 0.5

I believe AMHD policy is that you post your solution, people review and correct your answers.

This is not the post to which I responded. This "answer" was changed to conform to my post - again.