In statistics what does mutually exclusive mean?

Question

For homework a question related to Venn diagrams is 'Are the probabilities of having not used a spinner and not tossed a coin in the game mutually exclusive' Don't know what is meant by it so can't answer it with out your help

Answer 1

Two things ("events") are mutually exclusive if it is impossible for both to happen at the same time. For example, turning left and turning right are mutually exclusive.

A more probability-oriented example (with dice!) would be rolling a 6 and rolling an odd number. These are mutually exclusive. However, rolling a 6 and rolling an even number are not mutually exclusive.

As you are talking about Venn Diagrams, you might be thinking about "sample spaces" for events. For example,

• the sample space of even numbers (obtainable from rolling a die) is $E_{\text{even}}=\{2, 4, 6\}$, and $E_{\text{even}}\cap\{6\}=\{6\}$: The intersection of the sample spaces is non-empty. This means that the events are not mutually exclusive.

• the sample space of odd numbers (obtainable from rolling a die) is $E_{\text{odd}}=\{1, 3, 5\}$, and $E_{\text{odd}}\cap\{6\}=\emptyset$: The intersection of the sample spaces is empty. This means that the events are mutually exclusive.

Answer 2

Hint: two events are mutually exclusive if the occurrence of any one of them implies the non-occurrence of the other, or more formally if their intersection is empty. How can this concept be applied to the probabilities of having not used a spinner and not tossed a coin?

Answer 3

Two events, say $A$ and $B$, are mutually exclusive if and only if their intersection is empty: $A \cap B = \{\}$. This can be expressed alternatively as $|A \cap B| = 0$, or, in the language of a probabilist, $P (A \cap B) = 0$.