The probability that atleast one of the two events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, evaluate $P(\bar A) + P(\bar B)$.

We know that, $A \cup B$ denotes the occurrence of atleast one of A and B and $A \cap B$ denotes the occurrence of both A and B, simultaneously.

Thus, $P(A \cup B) = 0.6$ and $P(A \cap B) = 0.3$

Also, $P(A \cup B) = P(A) + P(B) - P(A \cap B)$

$\Rightarrow$ $0.6 = P(A) + P(B) - 0.3$

$\Rightarrow$ $P(A) + P(B) = 0.9$

$\Rightarrow$ $[1 - P(\bar A)] + [1 - P(\bar B)] = 0.9$

and $P(B) = 1 - P(\bar B)]$
$\Rightarrow$ $P(\bar A) + P(\bar B) = 2 - 0.9 = 1.1$