To calculate the probability of drawing an ace or a 9 from a standard deck of 52 playing cards, we’ll start by identifying the total number of favorable outcomes and the total number of possible outcomes.
A standard deck of cards contains:
- 4 aces (one from each suit: hearts, diamonds, clubs, spades)
- 4 nines (also one from each suit)
So, the total number of favorable outcomes for drawing either an ace or a 9 is:
- Number of aces: 4
- Number of nines: 4
Adding these together gives us:
- Total favorable outcomes = 4 (aces) + 4 (nines) = 8
Next, we consider the total number of possible outcomes, which is simply the number of cards in the deck:
- Total possible outcomes = 52 (the total number of cards)
Now, we can calculate the probability (P) of drawing an ace or a 9 using the formula:
- P(Ace or 9) = (Number of favorable outcomes) / (Total possible outcomes)
Substituting the values we have:
- P(Ace or 9) = 8 / 52
Simplifying this fraction:
- P(Ace or 9) = 2 / 13
Therefore, the probability of drawing an ace or a 9 from a well-shuffled deck of 52 cards is:
- 2/13 or approximately 0.1538 (15.38%)
This means that if you randomly draw a card from the deck, you have about a 15.38% chance of getting either an ace or a 9.