How to determine whether an event is Independent or Mutually Exclusive?

GRE Quant Problem Solving
1

This is a problem in the Probability chapter from the 5lb. book. It goes like this:
The probability of rain is 1/6 for any given day next week. What is the chance it rains on both Monday and Tuesday?

The two events are: Raining on Monday, and Raining on Tuesday. How are they independent, and not mutually exclusive?
The definition of a mutually exclusive event, according to the Math Review, “Events that cannot occur at the same time are said to be mutually exclusive.”

And these events seem to fit the description. It can’t rain on Monday and Tuesday at the same time.

Can somebody help me understand? Am I looking at events the wrong way?

2

The question does not say “same time”.

3

I think I’ve understood this.

I’ve been interpreting this differently. The mistake I’ve made is thinking “at the same time”, meaning it was Monday and Tuesday at the same time.

I found a better definition for Mutually Exclusive events on the web. It says “Two events are mutually exclusive if they cannot occur at the same time. If one event occurs, the other cannot occur.”.

So, Raining on Monday doesn’t prevent rain from occurring on Tuesday. So, the events can occur “simultaneously”.