Question

Two cards are drawn one after the other from a regular deck of 52 playing cards without replacement. The probability that the drawn cards are of different suits is

• A. \(\frac{39}{51}\)
• B. \(\frac{13}{52}\)
• C. \(\frac{2}{52}\)
• D. \(\frac{2}{51}\)

Hint:

When calculating probabilities involving multiple events, ensure to adjust the number of favorable outcomes for subsequent selections, especially in cases like without replacement.

Answer 1

The Correct Option is A

- In a deck of 52 cards, there are 13 cards in each suit. The first card can be any card from the deck, so there are 52 choices for the first card.
- For the second card, to ensure it is of a different suit, there are 39 cards remaining from the other three suits.
- Hence, the probability that the two cards are of different suits is:
\[ \frac{39}{51} = \frac{39}{52 - 1} = \frac{39}{51} \]