# Non/Not Mutually exclusive

Can both happen (at the same time)

Mutually exclusive - Time - Can't both happen

(at the same time) (see previous definition)

So Non/Not Mutually Exclusive - Time - CAN

both happen at the same time

Non/not mutually exclusive is the opposite to mutually exclusive.

**Example**

If a die is rolled find the probability of rolling a number less than 3 or an even number.

`Remember\ probability\=(N\umber\ of\ RIGHT\ answers)/(N\umber\ of \ALL\ possibl\e\ answers`

Start by drawing a probability tree for a roll of the dice that gives less than 3:

`1/6+1/6=2/6`

Now draw the probability tree for even numbers:

`1/6+1/6+1/6=3/6`

So `2/6+3/6=5/6`

But note the probability of getting 2 comes up twice, i.e.

A Venn diagram shows the problem:

In these cases you have to remove one of the crossovers to get the answer.

Add up `2/6+3/6` **but** remove `1/6`

`2/6+3/6=5/6`

`5/6-1/6=4/6`

`4/6=2/3`

**Answer: **

The probability of rolling a number less than 3 or an even number is 2 in 3 or 0.67.

And if 1 = 100% then 0.67 = 67% chance.

**Example 2**

What is the probability of you picking an ace or a heart from a pack of cards?

`Remember\ probability\=(N\umber\ of\ RIGHT\ answers)/(N\umber\ of \ALL\ possibl\e\ answers`

For 1 card probability = `1/52`

Start by drawing a probability tree:

## For Aces:

`1/52+1/52+1/52+1/52=4/52`

## For Hearts:

`1/52+1/52+1/52+1/52+1/52+1/52+1/52+1/52+1/52+1/52+1/52+1/52+1/52=13/52`

But note the ace of hearts is in both.

So remove one of the ace of hearts.

So total = `4/52+13/52-1/52`

So total = `(4+13-1)/52=16/52`

`16/52=8/26=4/13`

**Answer: **

The probability of picking an ace or a heart from a pack of cards is 4 in 13 or 0.308.

And if 1 = 100% then 0.308 = 30.8% chance.