Decide whether the two events listed are independent R is th

Decide whether the two events listed are independent:

R is the event that it rains in the Amazon jungle and H is the event that an instructor in New York City writes a difficult exam

Solution

This is purely qualitative question regarding the independence of two events: R - it rains in the Amazon jungle and H - an instructor in New Yord writes a difficult exam.

Two events are said to be independent if the occurence of one does not affect the occurence of the other.

Suppose an instructor in New Yord does write a difficult exam. That is, the event H happens.

In no way does this event change the possibility of rainfall in the amazon jungle. Weather conditions in a different part of the world will not be affected by the event H.

Therefore, the occurence of H does not affect the occurence of R.

Hence, we can say that the event H and R are independent.