Question

The probability that at least one of the events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.2, then \( P(A) + P(B) \) is:

• A. 0.4
• B. 0.8
• C. 1.2
• D. 1.4

Hint:

When given probabilities of the union and intersection of events, use the formula \( P(A \cup B) = P(A) + P(B) - P(A \cap B) \) to solve for the sum of the probabilities.

Answer 1

The Correct Option is C

Step 1: Understanding the given data.
We are given the following information: - The probability that at least one of events A and B occurs is 0.6. This can be written as: \[ P(A \cup B) = 0.6. \] - The probability that A and B occur simultaneously is 0.2. This can be written as: \[ P(A \cap B) = 0.2. \]
Step 2: Using the formula for the union of two events.
The formula for the union of two events is: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B). \] Substituting the given values into the formula: \[ 0.6 = P(A) + P(B) - 0.2. \]
Step 3: Solving for \( P(A) + P(B) \).
Now, solving for \( P(A) + P(B) \): \[ P(A) + P(B) = 0.6 + 0.2 = 1.2. \]
Step 4: Conclusion.
Therefore, the value of \( P(A) + P(B) \) is 1.2. The correct answer is (c) 1.2.