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

To find \( P(\bar{A}) + P(\bar{B}) \), let's start by using the formula for the probability of the union of two events: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]

Given:

• \( P(A \cup B) = 0.6 \)
• \( P(A \cap B) = 0.2 \)

Substituting these values into the formula, we have:

\(0.6 = P(A) + P(B) - 0.2\)

Simplifying this, we get:

\(P(A) + P(B) = 0.6 + 0.2 = 0.8\)

Now, we know:

• \( P(\bar{A}) = 1 - P(A) \)
• \( P(\bar{B}) = 1 - P(B) \)

Thus, \( P(\bar{A}) + P(\bar{B}) = (1 - P(A)) + (1 - P(B)) \)

\(= 2 - (P(A) + P(B))\)

Substituting \( P(A) + P(B) = 0.8 \) into this equation, we get:

\(P(\bar{A}) + P(\bar{B}) = 2 - 0.8 = 1.2\)

Therefore, the option 1.2 is correct.