Math Problem Statement

If P(A) = 0.59, P(B) = 0.6, and P(A and B) = 0.43, find P(A or B).

Solution

The problem in the image is asking to find P(A or B)P(A \text{ or } B), given the following probabilities:

  • P(A)=0.59P(A) = 0.59
  • P(B)=0.60P(B) = 0.60
  • P(A and B)=0.43P(A \text{ and } B) = 0.43

We can use the Addition Rule of Probability to solve this. The formula for the probability of the union of two events AA and BB is:

P(A or B)=P(A)+P(B)P(A and B)P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)

Substitute the given values:

P(A or B)=0.59+0.600.43P(A \text{ or } B) = 0.59 + 0.60 - 0.43

Let's calculate this.The probability P(A or B)P(A \text{ or } B) is 0.760.76.

Would you like more details or have any questions about this solution?

Here are 5 related questions to explore this further:

  1. What if P(A and B)P(A \text{ and } B) was 0? How would that change the result?
  2. How does the complement of P(A or B)P(A \text{ or } B) relate to this problem?
  3. Can we use this rule for more than two events, say for AA, BB, and CC?
  4. What does it mean if P(A and B)=P(A)×P(B)P(A \text{ and } B) = P(A) \times P(B)?
  5. How does the result change if events AA and BB are mutually exclusive?

Tip: The Addition Rule of Probability is useful for finding the probability

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Math Problem Analysis

Mathematical Concepts

Probability
Addition Rule of Probability

Formulas

P(A or B) = P(A) + P(B) - P(A and B)

Theorems

Addition Rule of Probability

Suitable Grade Level

Grades 9-12