# One card is selected at random from a deck of cards. What is the probability that the card selected is a spade or a queen?

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Whenever you solve a probability question involving two conditions, and you are being asked to find the probability that either will occur for a given action, you are looking for what is known as a "union probability". Formally speaking, if we say

The trick here is that these two possible events are not disjoint events; in other words, it **can** be possible to pull a single card and have it be a Spade and a Queen at the same time. The formula for determining

(This is read as "the probability of A union B is equal to the probability of A plus the probability of B minus the probability of the intersection of A and B".)

If we consider

If we consider

However, the probability **and** a Queen at the same time. Of all 52 cards in the deck, there is only one Queen of Spades, thus

Thus:

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