# Could we use the special addition rule for determining the probability that for one draw from a deck of cards, that the card is either a Queen or a Heart? Why or why not?

##### 1 Answer

You can't, because the probabilities are **not mutually exclusive.**

The addition rule is meant for **either...or** situations, and you even use that in your question. But not rightly so.

Event group 1: Queen

Event group 2: Heart

*But what about the queen of hearts?*

That's in both groups of events, so if you add you count it double.

Let's make the calculation:

Probability is defined as number of successes divided by total number of possibilities.

Total number of cards

Number of hearts ( **in** -cluding

Number of queens ( **ex** -cluding

(you can do the in- or ex-cluding the other way around)

Number of 'favourable' cards =

Total probability:

(simple adding would have led you to: