The problem is asking for the probability of getting either the same number on both dice or a sum of 5 when rolling two dice, one red and one white.

Step 1: Possible Outcomes

There are 6 faces on each die, so there are a total of $6 \times 6 = 36$ possible outcomes when rolling two dice.

Step 2: Favorable Outcomes

1. Same Number on Both Dice: The pairs (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6) are all possibilities. There are 6 such outcomes.

2. Sum of 5:

   • (1,4)
   • (2,3)
   • (3,2)
   • (4,1)

   These give us a total of 4 outcomes.

Step 3: Combining Favorable Outcomes

We now need to combine these two conditions. Notice that none of the outcomes where the dice show the same number also have a sum of 5, so we can simply add the two counts together.

• Total favorable outcomes = 6 (same numbers) + 4 (sum of 5) = 10 outcomes.

Step 4: Calculate Probability

The probability is the number of favorable outcomes divided by the total number of possible outcomes:

$\text{Probability} = \frac{10}{36} = \frac{5}{18}$

Answer

The correct answer is e. $\frac{5}{18}$.

Would you like any details or have any further questions?

Here are 5 related questions to consider:

1. What is the probability of rolling a sum of 7 with two dice?
2. How many possible outcomes result in a sum of 10?
3. What is the probability of rolling two dice and getting a sum of 2 or 12?
4. If you roll three dice, what is the probability that all three will show the same number?
5. How does the probability change if the dice are biased?

Tip: Always check if events overlap (i.e., double-counting) when calculating probabilities for combined events like this.