To determine the probability of randomly selecting an even numbered black card from a standard deck of 52 playing cards, we first need to identify the relevant cards.
In a standard deck, the black cards consist of spades and clubs. Each of these suits contains the following even numbered cards: 2, 4, 6, 8, and 10. Thus, there are a total of 5 even numbered black cards in each suit.
Since there are two black suits, we multiply the number of even cards in one suit by 2: 5 (from spades) + 5 (from clubs) = 10 even numbered black cards.
Next, we calculate the total number of cards in the deck, which is 52. The probability of drawing an even numbered black card can then be calculated using the formula:
Probability = (Number of favorable outcomes) / (Total outcomes)
Substituting the values we have:
Probability = 10 / 52
To simplify this fraction, we divide both the numerator and the denominator by 2, resulting in:
Probability = 5 / 26
Therefore, the probability of randomly selecting an even numbered black card from a standard deck of 52 playing cards is 5/26.