Final answer:
To determine the number of ways to choose an ace or a red card from a standard 52-card deck, we use the principle of inclusion-exclusion: count all red cards (26), add the aces (4), and subtract the red aces counted twice (2), resulting in 28 distinct ways.
Step-by-step explanation:
When calculating the number of ways you can choose an ace or a red card from a standard 52-card deck, we must take into account that there are 4 aces (one in each suit) and 26 red cards (13 hearts and 13 diamonds). However, two of the aces are also red cards (hearts and diamonds), so they have been counted twice if we were to simply add these counts together.
To find the correct total number of distinct ways to choose an ace or a red card, we use the principle of inclusion-exclusion:
- First, we count all the red cards, which totals 26.
- Then, we add the number of aces, which is 4.
- Next, we subtract the number of cards that have been counted twice, which is the red aces, and there are 2 of these (ace of hearts and ace of diamonds).
Therefore, the calculation is 26 (red cards) + 4 (aces) - 2 (red aces) = 28 distinct ways to choose either an ace or a red card. This kind of problem is a classic example of combinatorial reasoning, which often appears in probability and statistics topics within high school mathematics courses.