1. Problem: Find the probability of drawing a card with an odd number or a prime number from an ordinary deck. 2. Step 1: Determine the total number of cards in the deck. An ordinary deck has 52 cards. 3. Step 2: Identify cards with odd numbers. Number cards are from 2 to 10 plus face cards. Odd numbers are 3, 5, 7, 9. Each number appears in 4 suits so total odd number cards = $4 \times 4 = 16$. 4. Step 3: Identify cards with prime numbers. Prime numbers from 2 to 10 are 2, 3, 5, 7. Each appears in 4 suits so total prime number cards = $4 \times 4 = 16$. 5. Step 4: Calculate the cards that are both odd and prime to avoid double counting. These are 3, 5, 7, each with 4 suits. So cards both odd and prime = $3 \times 4 = 12$. 6. Step 5: Use the formula for union of two events: $$P(odd \cup prime) = P(odd) + P(prime) - P(odd \cap prime)$$ 7. Step 6: Calculate probabilities: $$P(odd) = \frac{16}{52}$$ $$P(prime) = \frac{16}{52}$$ $$P(odd \cap prime) = \frac{12}{52}$$ 8. Step 7: Plug values into formula: $$P = \frac{16}{52} + \frac{16}{52} - \frac{12}{52} = \frac{20}{52} = \frac{5}{13}$$ 9. Final answer: The probability of drawing a card with an odd number or a prime number is $\frac{5}{13}$.