Describe the following event as a subset of the set of all outcomes. If a deck of 52 cards is divided into two colors (red and black) and 4 suits (the red suits diamonds and hearts and the black suits spades and clubs) with 13 different values per suit (Ace, numbers 2 through 10, Jack, Queen, and King), then list the outcomes for drawing a face card with a man on it.

A. {Jack Hearts, King Hearts}
B. {Jack Hearts, Jack Spades, King Hearts, King Spades}
C. {King Hearts, King Diamonds, King Clubs, King Spades}
D. {Jack Hearts, Jack Diamonds, Jack Clubs, Jack Spades, King Hearts, King Diamonds, King Clubs, King Spades}

1 answer

To determine the outcomes for drawing a face card with a man on it from a standard deck of 52 cards, we first identify what constitutes a face card with a man on it:

In a standard deck:

  • The face cards include Jacks, Queens, and Kings.
  • The only face cards with a man depicted on them are the Jacks and Kings.

From the four suits (hearts, diamonds, clubs, and spades), the face cards with a man on them are:

  • Jacks: Jack of Hearts, Jack of Diamonds, Jack of Clubs, Jack of Spades
  • Kings: King of Hearts, King of Diamonds, King of Clubs, King of Spades

Now, we can compile the complete list of face cards with a man:

  • Jack of Hearts
  • Jack of Diamonds
  • Jack of Clubs
  • Jack of Spades
  • King of Hearts
  • King of Diamonds
  • King of Clubs
  • King of Spades

Thus, the outcomes for drawing a face card with a man on it are: \[ { \text{Jack Hearts}, \text{Jack Diamonds}, \text{Jack Clubs}, \text{Jack Spades}, \text{King Hearts}, \text{King Diamonds}, \text{King Clubs}, \text{King Spades} } \]

Now, let's analyze the given options: A. {Jack Hearts, King Hearts} — Incorrect (incomplete) B. {Jack Hearts, Jack Spades, King Hearts, King Spades} — Incorrect (incomplete, does not include diamonds and clubs) C. {King Hearts, King Diamonds, King Clubs, King Spades} — Incorrect (missing Jacks) D. {Jack Hearts, Jack Diamonds, Jack Clubs, Jack Spades, King Hearts, King Diamonds, King Clubs, King Spades} — Correct (includes all appropriate cards)

Therefore, the correct answer is: D. {Jack Hearts, Jack Diamonds, Jack Clubs, Jack Spades, King Hearts, King Diamonds, King Clubs, King Spades}