Final Answer:
The student's question addresses the concept of probability in mathematics. It involves calculating the probability of events within a sample space when conducting an experiment, such as rolling a die, where probabilities range from 0 (impossible) to 1 (certain).
Explanation:
The question involves the subject of probability, which is a branch of mathematics focused on the study of how likely events are to occur. The probability of an event is expressed as a number between zero and one, inclusive, where zero indicates impossibility and one indicates certainty. The sample space (S) is the set of all possible outcomes of a random experiment. Events are specific outcomes or sets of outcomes from the sample space to which probabilities are assigned.
If we roll a fair, six-sided die, the sample space S = {1, 2, 3, 4, 5, 6}. Let's say event A is the event of rolling an even number, then A = {2, 4, 6}. The probability of event A is calculated by dividing the number of favorable outcomes by the total number of outcomes in the sample space. Thus, P(A) = 3/6 = 1/2.
Example of Calculating Probability
Let's calculate the probability of rolling a number greater than four. We define the event B as the event of rolling a number greater than four, so B = {5, 6}. There are two favorable outcomes, and six possible outcomes in total: P(B) = 2/6 = 1/3.