In order to compute the theoretical probability of each event, you need to understand that probability is defined as the number of favorable outcomes divided by the total number of possible outcomes. In a standard 52-card deck, there are 52 unique cards. Let's calculate the probability for each event described:
**a) You draw a seven of diamonds:**
There is only one seven of diamonds in a 52-card deck.
- Favorable outcomes: 1 (the seven of diamonds)
- Total possible outcomes: 52 (total number of cards)
Therefore, the probability is:
P(seven of diamonds) = Number of favorable outcomes / Total number of possible outcomes
P(seven of diamonds) = 1 / 52
**b) You draw an ace:**
There are 4 aces in a 52-card deck, one for each suit.
- Favorable outcomes: 4 (the aces of hearts, diamonds, clubs, and spades)
- Total possible outcomes: 52 (total number of cards)
Thus, the probability is:
P(ace) = Number of favorable outcomes / Total number of possible outcomes
P(ace) = 4 / 52
P(ace) = 1 / 13 (simplifying the fraction by dividing both the numerator and the denominator by 4)
**c) You draw a numbered club:**
The clubs have 9 numbered cards (2 through 10).
- Favorable outcomes: 9 (the 2, 3, 4, 5, 6, 7, 8, 9, and 10 of clubs)
- Total possible outcomes: 52 (total number of cards)
So, the probability is:
P(numbered club) = Number of favorable outcomes / Total number of possible outcomes
P(numbered club) = 9 / 52
**d) You draw an even-numbered card of any suit:**
Each suit has 5 even-numbered cards: 2, 4, 6, 8, and 10. There are 4 suits, so there are 20 even-numbered cards in total.
- Favorable outcomes: 20 (five even-numbered cards in each of the four suits)
- Total possible outcomes: 52 (total number of cards)
Therefore, the probability is:
P(even-numbered card) = Number of favorable outcomes / Total number of possible outcomes
P(even-numbered card) = 20 / 52
P(even-numbered card) = 5 / 13 (simplifying the fraction by dividing both the numerator and the denominator by 4)
These are the theoretical probabilities for each of the events described.
