Final answer:
The probability of randomly selecting a club or a 5 from a standard deck of 52 cards is 4/13, after accounting for the 5 of clubs which is included in both categories.
Step-by-step explanation:
To calculate the probability of selecting either a club or a 5 from a well-shuffled standard deck of 52 cards, we can break this down into two separate events and make sure not to double-count the 5 of clubs, which would fall into both categories. A standard deck has four suits: clubs, diamonds, hearts, and spades, each with 13 cards, including the numbers 1 through 10, and the face cards J (jack), Q (queen), and K (king).
First, let's find the probability of drawing a club. There are 13 clubs in a deck of 52 cards, so the probability of drawing a club is 13/52. Next, we consider the probability of drawing a 5. There are four 5s in the deck (one for each suit), so normally the probability would be 4/52. However, since we've already counted the 5 of clubs, we must subtract that from our count, leaving us with only three additional 5s that are not clubs. This gives us a probability of 3/52 for drawing a 5 that is not a club. Lastly, we add the two probabilities together to find the total probability of drawing either a club or a 5.
Total probability = Probability of a club + Probability of a 5 not being a club = (13/52) + (3/52) = 16/52, which reduces to 4/13.
Therefore, the reduced fraction representing the probability of drawing either a club or a 5 from a standard deck of cards is 4/13.