If you roll a pair of dice, what is the probability of rolling either a single 3 or a sum that is an odd number?

In this task we have to calculate the probability of sum of 2 events (i.e. rolling a single 3 or rolling an odd sum).

To do this we must use the following formula:

Now we can use the first formula:

To find the probability of rolling either a single 3 or a sum that is an odd number when rolling a pair of dice, we first need to determine the total number of favorable outcomes and the total number of possible outcomes.

Total number of possible outcomes when rolling a pair of dice = (6 \times 6 = 36)

Now, let's find the number of favorable outcomes:

1. Rolling a single 3: There are two ways to achieve this outcome, either by rolling a 3 on the first die and any other number on the second die, or by rolling any other number on the first die and a 3 on the second die. So, there are 2 favorable outcomes.

2. Rolling a sum that is an odd number: Out of the 36 possible outcomes, there are 18 outcomes where the sum is odd (1+2, 1+4, 1+6, 2+1, 2+3, 2+5, 3+1, 3+2, 3+4, 3+6, 4+1, 4+3, 4+5, 5+2, 5+4, 5+6, 6+1, 6+3, 6+5).

Now, let's find the probability:

Total number of favorable outcomes = (2 + 18 = 20)

Probability of rolling either a single 3 or a sum that is an odd number = (\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{20}{36} = \frac{5}{9})

Therefore, the probability of rolling either a single 3 or a sum that is an odd number when rolling a pair of dice is ( \frac{5}{9}).