Final answer:
The probability of rolling a 2 or an odd number on a six-sided die is the combined events of rolling a 2 or an odd number (1, 2, 3, 5), resulting in a probability of 4/6, which simplifies to 2/3 or about 0.667.
Step-by-step explanation:
The question revolves around finding the probability of rolling a 2 or an odd number on a single six-sided die. To find the probability of either event occurring, we'll first identify the sample space and the favorable outcomes. The sample space of a six-sided die is S = {1, 2, 3, 4, 5, 6}.
An odd number from a die roll can be 1, 3, or 5. So, the favorable outcomes for rolling an odd number, event A, is A = {1, 3, 5}. The outcome for rolling a two, event B, is B = {2}. When we combine the two events, since 2 is not an odd number, we simply merge the outcomes to get the combined event A OR B = {1, 2, 3, 5}. Therefore, we have four favorable outcomes. The probability of an event is calculated by dividing the number of favorable outcomes by the number of all possible outcomes, which in this case is 6.
The probability of rolling a 2 or an odd number is then 4 out of 6, or written as a fraction, 4/6, which simplifies to 2/3 or approximately 0.667. This means that there's a two-thirds chance that rolling the die once will result in either a 2 or an odd number.