Question

A card is drawn at random from a well shuffled pack of 52 cards. What is the probability of getting a ‘two’ of hearts or a ‘three’ of diamonds ?

• A. \(\frac{2}{13}\)
• B. \(\frac{5}{13}\)
• C. \(\frac{1}{26}\)
• D. \(\frac{5}{26}\)

Answer 1

The Correct Option is C

To find the probability of drawing a 'two' of hearts or a 'three' of diamonds from a deck of 52 cards, we need to analyze the possible outcomes. In a standard deck of 52 cards, there is exactly one 'two' of hearts and one 'three' of diamonds. These are two distinct cards, so the events of drawing either of these cards are mutually exclusive.

The probability \( P \) of an event can be calculated using the formula:

$$ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} $$

In this case, the number of favorable outcomes is 2 (one 'two' of hearts and one 'three' of diamonds), and the total number of possible outcomes is 52, as there are 52 cards in the deck.

Therefore, the probability of drawing a 'two' of hearts or a 'three' of diamonds is:

$$ P = \frac{2}{52} = \frac{1}{26} $$

Hence, the correct answer is \(\frac{1}{26}\).