If two six-sided dice are rolled, what is the probability that the total number of spots showing is

an odd number?

Verified step by step guidance

1. <span>Step 1: Understand the problem. We need to find the probability that the sum of the numbers on two six-sided dice is an odd number.</span>
2. <span>Step 2: Determine the total number of possible outcomes when two dice are rolled. Since each die has 6 faces, the total number of outcomes is 6 \times 6 = 36.</span>
3. <span>Step 3: Identify the condition for the sum to be odd. The sum of two numbers is odd if one number is even and the other is odd.</span>
4. <span>Step 4: Calculate the number of favorable outcomes. For each die, there are 3 even numbers (2, 4, 6) and 3 odd numbers (1, 3, 5). Consider the combinations: (even, odd) and (odd, even).</span>
5. <span>Step 5: Calculate the probability. Add the number of favorable outcomes from both combinations and divide by the total number of outcomes (36) to find the probability.</span>

Key Concepts

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a ratio of favorable outcomes to the total number of possible outcomes. In the context of rolling dice, it helps determine how likely it is to achieve a specific sum, such as an odd number, when two dice are rolled.

Outcomes of Rolling Dice

When rolling two six-sided dice, each die has six faces, leading to a total of 36 possible outcomes (6 faces on the first die multiplied by 6 faces on the second die). Each outcome corresponds to a unique combination of the numbers showing on the two dice, which is essential for calculating probabilities.

Odd and Even Sums

The sum of two numbers can be either odd or even. An odd sum occurs when one die shows an odd number and the other shows an even number. Understanding how to categorize the sums based on the parity of the numbers rolled is crucial for determining the probability of obtaining an odd total when rolling two dice.