In a standard deck of cards, what is the probability of drawing an ace OR a black card (answer choices are in the form of a percentage, rounded to the nearest whole number)

In a standard deck of cards, what is the probability of drawing an ace OR a black card (answer choices are in the form of a percentage, rounded to the nearest whole number)?

A.) 25%

B.) 50%

C.) 54%

D.) 33%

The correct answer and explanation is:

Correct Answer: C.) 54%

To determine the probability of drawing an ace or a black card from a standard deck of 52 cards, we use the principle of inclusion and exclusion. This principle avoids counting overlapping outcomes more than once.

There are two parts to this problem:

1. Number of aces in a deck:
   There are 4 aces in a standard deck (one per suit).
2. Number of black cards in a deck:
   There are 26 black cards (13 spades and 13 clubs).

However, 2 of the aces are black (Ace of spades and Ace of clubs), so if we simply added the number of aces and black cards (4 + 26), we would be double-counting those 2 black aces.

So we apply the formula:

P(A or B) = P(A) + P(B) – P(A and B)

Let:

• A = drawing an ace = 4 cards
• B = drawing a black card = 26 cards
• A and B = drawing a black ace = 2 cards

So,

• Favorable outcomes = 4 (aces) + 26 (black cards) – 2 (black aces) = 28

Now we calculate the probability:

P(ace or black card) = 28 / 52

Convert to a percentage:

28 ÷ 52 ≈ 0.5385 → 53.85%, which rounds to 54%

Therefore, the correct answer is C.) 54%

This means that in a single random draw from a standard deck, there is a 54 percent chance that the card drawn will either be an ace or a black card. Understanding how overlapping categories work is essential in probability, especially when dealing with sets that are not mutually exclusive.