To determine the probability that a football game between teams P and Q ends in a draw, we need to understand the basic principles of probability and how they apply to this scenario. ### Step-by-Step Explanation 1. **Understanding Probability**: Probability is a measure of the likelihood of an event occurring. It is calculated using the formula: \[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \] where \( P(E) \) is the probability of event \( E \). 2. **Identifying Possible Outcomes**: In a football match, there are typically three possible outcomes: - Team P wins - Team Q wins - The game ends in a draw Therefore, the total number of possible outcomes is 3. 3. **Favorable Outcomes for a Draw**: The favorable outcome for the event "the game ends in a draw" is just one: the game can end in a draw. Thus, the number of favorable outcomes for a draw is 1. 4. **Calculating the Probability of a Draw**: Using the probability formula: \[ P(\text{Draw}) = \frac{\text{Number of favorable outcomes for a draw}}{\text{Total number of possible outcomes}} = \frac{1}{3} \] 5. **Conclusion**: Therefore, the probability that the game ends in a draw is \( \frac{1}{3} \). ### Evaluating the Options Now, let's evaluate the provided options: - **Option A: \( \frac{2}{3} \)**: This suggests that there is a 66.67% chance of a draw, which is incorrect because it implies that draws are more likely than any other outcome, which contradicts our calculation. - **Option B: \( \frac{1}{2} \)**: This indicates a 50% chance of a draw, which is also incorrect. This would imply that draws and one of the other outcomes (either a win for P or Q) are equally likely, which is not supported by our analysis. - **Option C: \( \frac{1}{3} \)**: This is the correct answer, as we calculated that there is one favorable outcome (a draw) out of three possible outcomes. - **Option D: \( \frac{1}{4} \)**: This suggests a 25% chance of a draw, which is incorrect. This would imply that there are four possible outcomes, which is not the case in a standard football match. ### Summary of Key Points - The total number of possible outcomes in a football match is 3: win for P, win for Q, or a draw. - The number of favorable outcomes for a draw is 1. - The probability of a draw is calculated as \( \frac{1}{3} \). - The correct answer is Option C: \( \frac{1}{3} \). ### Revision Summary - Probability is calculated as the number of favorable outcomes divided by the total number of possible outcomes. - In a football match, there are three outcomes: win for P, win for Q, and draw. - The probability of a draw is \( \frac{1}{3} \). - Always evaluate each option against the calculated probability to identify the correct answer.