Final answer:
The probability of an event in a uniform probability space is calculated by dividing the number of favorable outcomes for the event by the total number of possible outcomes. For example, when rolling a six-sided die, if event A is rolling a 2 or a 3, the probability P(A) is 2/6 or 1/3.
Step-by-step explanation:
To calculate the probability of an event A when all outcomes in the sample space are equally likely, you count the number of favorable outcomes for event A and divide by the total number of outcomes in the sample space. The probability is known as the theoretical probability of A.
For example, let's consider rolling a fair, six-sided die. The sample space S = {1, 2, 3, 4, 5, 6}. If event A is defined as rolling a 2 or a 3, then A = {2, 3}. The probability of event A, P(A), would be the number of outcomes in A divided by the total outcomes in S, so P(A) = 2/6 or 1/3 since there are 2 favorable outcomes out of 6 possible outcomes.
If we consider another event B = numbers greater than 13 from the sample space of whole numbers starting at one and less than 20, then event B = {14, 15, 16, 17, 18, 19}. Thus, P(B), the probability of B, would be 6/19 because there are 6 outcomes that are greater than 13 out of a total of 19 outcomes from 1 to 18.