Step-by-step Solution:

We are given the following information: \[\] \(P(A \cup B) = 0.6\), which is the probability that at least one of the events \(A\) or \(B\) occurs. - \(P(A \cap B) = 0.3\), which is the probability that both \(A\) and \(B\) occur simultaneously. We are asked to find \(P(A') + P(B')\), where \(A'\) and \(B'\) are the complements of \(A\) and \(B\), respectively. \[\] Step 1: Use the formula for the probability of the union of two events The probability of the union of two events is given by the formula: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \] Substitute the known values: \[ 0.6 = P(A) + P(B) - 0.3 \] Solving for \(P(A) + P(B)\): \[ P(A) + P(B) = 0.6 + 0.3 = 0.9 \] \[\] Step 2: Use the complement rule The sum of the probabilities of the complements of \(A\) and \(B\) is: \[ P(A') + P(B') = 1 - P(A) + 1 - P(B) \] This simplifies to: \[ P(A') + P(B') = 2 - (P(A) + P(B)) \] Substitute \(P(A) + P(B) = 0.9\) into the equation: \[ P(A') + P(B') = 2 - 0.9 = 1.1 \] \[\] Final Answer: The correct answer is C. 1.1.