Geometry

Question Analysis
This question involves calculating the probability of non - mutually exclusive events using a standard deck of cards.
The main focus is on determining the number of cards in each event (drawing a spade and drawing an even - numbered card), finding the number of cards in their intersection, and applying the formula for non - mutually exclusive events to obtain the correct probability.

Key Concept Explanation
The formula is applied here. Event A is drawing a spade, and event B is drawing an even - numbered card.
The subtraction of is essential because there are even - numbered spades (2, 4, 6, 8, 10 of spades) that would be double - counted if only the probabilities of the individual events were added.

Step-by-Step Solution
Calculate the number of spades in a deck: There are 13 spades, so .
Calculate the number of even - numbered cards in a deck: There are 5 even - numbered ranks (2, 4, 6, 8, 10) in each of the 4 suits, so there are even - numbered cards. Thus, .
Determine the number of cards that are both spades and even - numbered: There are 5 such cards (2, 4, 6, 8, 10 of spades), so

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