Final answer:
The formula for calculating the probability of an event occurring in an equally-likely probability model is 'P(event) = Number of favorable outcomes / Total number of outcomes.' This formula applies when each outcome has the same chance of occurring, such as rolling a die or flipping a coin.
Step-by-step explanation:
Understanding the Equally-Likely Model of Probability
The formula for calculating the probability of an event occurring in an equally-likely model of probability is given as:
P(event) = Number of favorable outcomes / Total number of outcomes
This formula corresponds to choice A in the options provided by the student. When we refer to equally likely outcomes, we imply that each outcome in the sample space has the same chance of occurring. For instance, when tossing a fair, six-sided die, each face has an equal chance to land on top; hence, the probability of any given face is 1 out of 6.
To illustrate, consider event B, defined as the event where the sum of two dice rolls is at most seven. To find P(B), you would need to count the number of outcomes where the sum is seven or less and then divide by the total number of possible outcomes when two dice are rolled (36). Similarly, for events that are not equally likely, additional concepts apply, such as conditional probability P(A|B), which considers the reduced sample space after an event B has occurred.
It's important to distinguish between independent and mutually exclusive events. For instance, if we have P(A AND B) = 0.15, this provides us with the joint probability for two independent events occurring together. Additionally, if P(A) + P(B) > 1, the events cannot be mutually exclusive because their probabilities would exceed 100% when combined.
Fundamentally, the probability of any event can range from 0 (the event never happens) to 1 (the event always happens), reflecting the inherent uncertainty and variability within different types of events and outcomes.