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In probability, when we talk about mutually exclusive events, we refer to events that cannot occur at the same time. For example, when rolling two dice, you cannot get a sum of both 7 and 11 at the same time from a single roll.
Hence, these outcomes are considered mutually exclusive.

If two events are mutually exclusive, it means that the occurrence of one event means the other cannot occur in that instance. This is an important concept when calculating probabilities because it helps us understand how different events relate
to one another. Mutual exclusivity simplifies calculations since the joint probability of both occurring is zero.

Understanding mutually exclusive events helps pave the way for determining the probability of either event happening by using the rule:

• If events A and B are mutually exclusive, \(P(A \text{ or } B) = P(A) + P(B)\).

Rolling dice is a classic example that helps illustrate various concepts in probability. When we roll two dice, each die has 6 faces, usually numbered from 1 to 6.
The total number of possible outcomes when rolling two dice is calculated by multiplying the number of outcomes for each die: \(6 \times 6 = 36\).
The outcomes of interest in dice rolls are often specific sums of the numbers appearing on each die. For instance, if you need to find the combinations that lead to specific sums, like 7 or 11, you list out all the pairs of numbers that add up to those sums. Each pair is considered a unique outcome. For a sum of 7, pairs like (1,6), (2,5), etc., are considered.
Knowing all the possible outcomes and identifying the combinations that lead to particular sums is the first step in calculating probabilities based on these outcomes.

To calculate the probability of an event, you divide the number of successful outcomes by the total number of possible outcomes. This simple ratio gives you a chance of an event occurring.
For example, calculating the probability of rolling a sum of 7 on two dice involves first identifying all possible die combinations for that sum, numbering 6 in total.
The probability then is \(\frac{6}{36} = \frac{1}{6}\), given there are 36 possible outcomes when rolling two dice. Similarly, there are 2 combinations for a sum of 11, so the probability is \(\frac{2}{36} = \frac{1}{18}\).

When dealing with mutually exclusive events, such as the sum of 7 or 11, you simply add their individual probabilities. This is possible because they cannot happen simultaneously:

• The probability of getting a sum of 7 or 11 is calculated as \(\frac{1}{6} + \frac{1}{18}\).
• This requires finding a common denominator to combine them into a single probability \(\frac{2}{9}\).

Thus, the calculations are streamlined using basic arithmetic rules, helping derive accurate probabilities for various outcomes.