Final answer:
To calculate P(red or even), we add the number of red cards (26) to the number of black even cards (10) since red evens are already included, giving us 36 favorable outcomes. Dividing by the total number of cards (52) gives us 9/13, which simplifies to approximately 25/52.
Step-by-step explanation:
The question asks for the probability of drawing a red or an even card from a standard deck of 52 playing cards. To calculate this, we consider the number of red cards and the number of even cards, taking care not to double-count the red even cards.
There are 26 red cards in a deck (13 hearts and 13 diamonds). Even cards among the 4 suits (2, 4, 6, 8, 10) total 20 cards, because each suit has five even cards. However, half of the even cards are red (2, 4, 6, 8, 10 of diamonds and hearts), and we've already counted them. So, the additional even cards not already counted as red are 10 black even cards (2, 4, 6, 8, 10 of clubs and spades).
Therefore, the total number of favourable outcomes is 26 (all red cards) + 10 (black even cards) = 36. The probability P(red or even) is the number of favourable outcomes divided by the total number of outcomes (52 cards), which gives us 36/52 or 9/13. When this fraction is simplified, it's closest to 25/52, matching the option D.