Problem 59 - College Algebra

Question

Explain how to find or probabilities with mutually exclusive events. Give an example.

Step-by-Step Solution

Answer

The 'or' probability of mutually exclusive events is calculated by adding the probabilities of each event. For example, when rolling a die, the probability of rolling a 3 or 4 can be calculated as \(P(3) + P(4) = 1/6 + 1/6 = 2/6 = 1/3\)

Step 1 - Understanding the concept of Mutually Exclusive Events

First, comprehend the concept of mutually exclusive events. As the name implies, 'mutually exclusive' means two events cannot happen at the same time. An example would be rolling a die, where it cannot land on both 3 and 4 simultaneously.

Step 2 - Calculating 'or' probabilities for Mutually Exclusive Events

The probability of either of two (or more) mutually exclusive events happening is calculated by simply adding the probabilities of each event. This is represented mathematically by P(A or B) = P(A) + P(B).

Step 3 - Give an example

Let's assume that A is the event of rolling a 3 and B is the event of rolling a 4 on a die. In a single roll, P(A) = 1/6 and P(B) = 1/6. So, the 'or' probability P(A or B) can be calculated as P(A) + P(B) = 1/6 + 1/6 = 2/6 = 1/3.