Lucy has a deck of 52 cards with 4 suits (hearts, spades, diamonds, and clubs), and each suit has cards numbered 1−13 . What is the theoretical probability of her picking a 4 from the deck of cards? The answer should be a fraction. Remember to simplify

1 answer

In a standard deck of 52 playing cards, there are 4 suits: hearts, spades, diamonds, and clubs. Each suit contains exactly one card numbered 4. Thus, there are a total of 4 cards that are 4s in the entire deck.

To find the theoretical probability of picking a 4 from the deck, we can use the formula for probability:

\[ P(\text{picking a 4}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \]

In this scenario:

  • The number of favorable outcomes (picking a 4) = 4
  • The total number of possible outcomes (total cards) = 52

So, the probability is:

\[ P(\text{picking a 4}) = \frac{4}{52} \]

Next, we simplify the fraction:

\[ \frac{4}{52} = \frac{1}{13} \]

Therefore, the theoretical probability of Lucy picking a 4 from the deck of cards is:

\[ \frac{1}{13} \]