Final answer:
The probability of rolling an odd or prime number when a single die is tossed is 2/3, as there are four favorable outcomes (1, 2, 3, 5) out of six possible outcomes.
Step-by-step explanation:
When a single die is rolled, the probability of rolling an odd number or a prime number can be calculated by considering the properties of the numbers on the die. The numbers 1, 2, 3, 4, 5, and 6 appear on the faces of the die, with the odd numbers being 1, 3, and 5, and the prime numbers being 2, 3, and 5. To find the probability of rolling either an odd or a prime number, we combine the outcomes for both conditions, which gives us the numbers 1, 2, 3, and 5.
The total number of possible outcomes when rolling a single die is six. The combined favorable outcomes for getting either an odd or a prime number are four: 1 (odd), 2 (prime), 3 (odd and prime), and 5 (odd and prime). The union of the sets A (prime) and B (odd) is {1, 2, 3, 5}. Therefore, the probability (P) is the number of favorable outcomes divided by the number of possible outcomes, which is P(A or B)=4/6 or 2/3 after simplifying.