Probability of an event with 2 scenarios How to determine probability if we have 2 scenarios.
For example
If 70% of men have black eyes &amp; 
60% of Indians have black eyes
What will be the chances of an Indian Man having black eyes?
The given information is insufficient. I will give two examples to show this. 

Case I - There are 300 Indians, 120 of them are men who do not have black eyes, and rest of the Indians are not men, but have black eyes. This satisfies the condition that 60% Indians have black eyes. There are 280 other men who are not Indians and have black eyes. Now, 70% of men have black eyes. In this case, no Indian man has black eyes.

Case II - There are 100 Indians, 60 of them men and having black eyes. Remaining 40 Indians are not men and do not have black eyes. Thus, 60% Indians have black eyes. There are 40 other men who are not Indians out of which 10 have black eyes, the remaining 30 do not have black eyes. Thus, 70% of men have black eyes. In this case, all Indian men have black eyes. 

So the answer can be anywhere between and including 0% and 100%.
It should be $60\% \cdot 70\%=42\%$