To find the probability of selecting an ace or a 9 from a standard 52-card deck, we first need to understand how many aces and 9s are present in the deck.
A standard deck of cards contains:
- 4 aces (one from each suit: hearts, diamonds, clubs, spades)
- 4 nines (one from each suit: hearts, diamonds, clubs, spades)
Since the events of drawing an ace and drawing a 9 are mutually exclusive (they cannot happen at the same time), we can simply add the probabilities of each event:
1. **Probability of selecting an ace**: There are 4 aces in the deck. Therefore, the probability of drawing an ace is:
P(Ace) = Number of Aces / Total Number of Cards = 4/52
2. **Probability of selecting a 9**: Similar to aces, there are also 4 nines in the deck. Thus, the probability of drawing a 9 is:
P(Nine) = Number of Nines / Total Number of Cards = 4/52
Now, we can combine both probabilities to find the total probability of selecting either an ace or a 9:
P(Ace or Nine) = P(Ace) + P(Nine) = (4/52) + (4/52)
Calculating that gives us:
P(Ace or Nine) = 8/52
This fraction can be simplified:
P(Ace or Nine) = 2/13
Thus, the probability of randomly selecting either an ace or a 9 from a standard 52-card deck is:
2/13 or approximately 0.1538 (15.38%)