What is the probability of an event E in a uniform sample space S?

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To calculate the probability of an event E in a uniform sample space S, you need to consider two factors: the number of outcomes that satisfy event E, and the total number of possible outcomes in sample space S.

First, you need to determine the number of outcomes that satisfy event E. This can vary depending on the specific event. For example, if event E is the event of rolling an even number on a fair six-sided die, then there are three outcomes that satisfy this event (2, 4, and 6).

Next, you need to calculate the total number of possible outcomes in the sample space S. In a uniform sample space, all outcomes have an equal chance of occurring. For example, if you are rolling a fair six-sided die, there are six possible outcomes (1, 2, 3, 4, 5, and 6).

Finally, you can calculate the probability of event E using the formula:

Probability of E = Number of outcomes satisfying E / Total number of possible outcomes

For example, using the previous example of rolling an even number on a fair six-sided die, the probability of event E would be:

Probability of E = 3 (number of outcomes satisfying E) / 6 (total number of possible outcomes) = 1/2 or 0.5

So, in this case, the probability of event E is 0.5 or 50%.