Points to Remember:
- Basic probability concepts: Probability is the likelihood of an event occurring. It’s calculated as the ratio of favorable outcomes to the total number of possible outcomes.
- Sample space of a die: A standard six-sided die has a sample space of {1, 2, 3, 4, 5, 6}.
- Even numbers: Even numbers are integers divisible by 2.
Introduction:
Probability is a fundamental concept in mathematics and statistics used to quantify the likelihood of an event. In this case, we are dealing with a simple probability problem involving the throw of a single, fair six-sided die. A fair die implies that each face (number 1 through 6) has an equal chance of appearing. We want to determine the probability of obtaining an even number in a single throw.
Body:
1. Defining the Event and Sample Space:
The event of interest is obtaining an even number. The sample space, representing all possible outcomes of a single die throw, is S = {1, 2, 3, 4, 5, 6}.
2. Identifying Favorable Outcomes:
The even numbers within the sample space are {2, 4, 6}. Therefore, there are 3 favorable outcomes.
3. Calculating the Probability:
The probability (P) of an event is calculated as:
P(Event) = (Number of favorable outcomes) / (Total number of possible outcomes)
In this case:
P(Even number) = 3 / 6 = 1/2 = 0.5
4. Interpretation:
The probability of getting an even number in a single throw of a fair six-sided die is 0.5 or 50%. This means that there’s an equal chance of getting an even number as there is of getting an odd number.
Conclusion:
In summary, the probability of obtaining an even number (2, 4, or 6) when throwing a fair six-sided die is 1/2 or 50%. This simple calculation demonstrates a fundamental principle of probability: the ratio of favorable outcomes to the total number of possible outcomes. Understanding basic probability is crucial in various fields, from games of chance to risk assessment and statistical analysis. This example highlights the importance of clearly defining the event and sample space for accurate probability calculations. Further exploration could involve more complex scenarios with multiple dice or weighted dice, leading to a deeper understanding of probability theory.
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