Final answer:
The Fundamental Counting Principle is used to calculate probabilities of independent events by multiplying their individual number of outcomes. The probability of both independent events occurring together (P(A AND B)) is found by multiplying their individual probabilities. The addition rule (P(A OR B)) accounts for the probability that at least one of the events will occur.
Step-by-step explanation:
The use of the Fundamental Counting Principle is crucial when determining the probabilities of independent events. The principle suggests that if you have two independent events, you can find the total number of possible outcomes by multiplying the number of outcomes for each event.
For example, if rolling a die (with 6 possible outcomes) and flipping a coin (with 2 possible outcomes) are independent events, their combined number of possible outcomes would be 6 * 2 = 12.
According to the principles of probability:
- The product rule states that for independent events, P(A AND B) = P(A)P(B). This means the probability of both events occurring together is the product of their individual probabilities.
- The addition rule states that P(A OR B) = P(A) + P(B) − P(A AND B). This allows us to calculate the probability that at least one of the two events will occur.
For example, if event A has a probability of 0.5 and event B has a probability of 0.3, and they are independent, then the probability of both A and B occurring would be P(A AND B) = 0.5 * 0.3 = 0.15.