Question

If 2 cards drawn at random from a well shuffled pack of 52 playing cards are from the same suit, then the probability of getting a face card and a card having a prime number is:

• A. \(\frac{8}{13}\)
• B. \(\frac{2}{13}\)
• C. \(\frac{8}{221}\)
• D. \(\frac{32}{221}\)

Hint:

For combined conditions in card games, count the individual items meeting each condition, then calculate the combined probabilities.

Answer 1

The Correct Option is B

Consider each suit separately, as the problem implies drawing both cards from the same suit. Face cards are Jack, Queen, King, and prime-numbered cards are 2, 3, 5, 7: \[ \text{Total cards in a suit:} 13 \] \[ \text{Face cards in a suit:} 3 \] \[ \text{Prime-numbered cards in a suit:} 4 \] Assuming no overlap between face and prime cards: \[ \text{Total ways to draw 2 specific types in the same suit:} \binom{13}{2} = 78 \] \[ \text{Probability of specific draw from one suit:} \frac{3 \times 4}{78} \] \[ \text{Corrected probability considering all suits:} \frac{12}{78} = \frac{2}{13} \]