Question

Probability of at least one of the events A and B occur is 0.6. If A and B occur simultaneously with probability 0.2, then $P(\bar{A}) + P(\bar{B})$ is

• A. 1
• B. 0.8
• C. 0.6
• D. 1.2

Hint:

A useful derived identity to remember for these specific questions is: $P(\bar{A}) + P(\bar{B}) = 2 - (P(A \cup B) + P(A \cap B))$. It jumps straight to the answer.

Answer 1

The Correct Option is D

Step 1: Given Data
\[ P(A \cup B) = 0.6, P(A \cap B) = 0.2 \]
Step 2: Use Addition Formula
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \] \[ 0.6 = P(A) + P(B) - 0.2 \] \[ P(A) + P(B) = 0.6 + 0.2 = 0.8 \]
Step 3: Use Complement Rule
\[ P(\bar{A}) = 1 - P(A), P(\bar{B}) = 1 - P(B) \] \[ P(\bar{A}) + P(\bar{B}) = (1 - P(A)) + (1 - P(B)) \] \[ = 2 - (P(A) + P(B)) \]
Step 4: Substitute Value
\[ P(\bar{A}) + P(\bar{B}) = 2 - 0.8 = 1.2 \]
Step 5: Final Answer
\[ \boxed{1.2} \]