# 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?

Feb 7, 2015

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 $= 52$
Number of hearts ( in -cluding $Q$ of hearts) =$13$
Number of queens ( ex -cluding $Q$ of hearts!!) = $3$
(you can do the in- or ex-cluding the other way around)

Number of 'favourable' cards = $16$

Total probability: $P = \frac{16}{52} = \frac{4}{13} \approx 0.308$

(simple adding would have led you to: $P = \frac{17}{52} \approx 0.327$)