Question

Pinochle is a card game played with a deck of 48 cards consisting of 2 Aces, 2 Kings, 2 Queens, 2 Jacks, 2 Tens, and 2 Nines in each of the four standard suits [hearts , diamonds, spades, and clubs]. If one card is drawn at random from this deck, what is the probability of

a. drawing an Ace
b. drawing a club
c. drawing a red card
d. drawing a face card (Jack, Queen, King)

Answer 1

In a Pinochle card game, the probabilities are 1/6 for drawing an Ace or a club, 1/3 for a red card, and 1/2 for a face card.

Step-by-step explanation:

When calculating probabilities in a game of Pinochle with a 48-card deck, the following approaches are used:

• Probability of drawing an Ace: There are 2 Aces of each suit in the deck, hence there are a total of 8 Aces. The probability of drawing an Ace is 8/48 or 1/6.
• Probability of drawing a club: There are 2 of each rank in clubs, amounting to 8 clubs in total. Thus, the probability of drawing a club is 8/48 or 1/6.
• Probability of drawing a red card: The red cards are diamonds and hearts. There are 8 red cards of each suit, which gives us 16 red cards in total. Therefore, the probability of drawing a red card is 16/48 or 1/3.
• Probability of drawing a face card (Jack, Queen, King): Each suit has 2 Jacks, 2 Queens, and 2 Kings, making it 6 face cards per suit. With four suits, this gives us 24 face cards in the deck. The probability of drawing a face card is 24/48 or 1/2.