If events A and B are independent, P(A) = 0.4, and P(B) = 0.5, what is P(A^c intersect B^c)?

We are given that events $A$ and $B$ are independent.
We are given the probabilities:
$P(A) = 0.4$
$P(B) = 0.5$

The probability of the complement of an event $E$, denoted $P(E^c)$, is $1 - P(E)$.
For event $A$:

For event $B$:

If events $A$ and $B$ are independent, then their complements $A^c$ and $B^c$ are also independent.
For independent events $E_1$ and $E_2$, the probability of their intersection is $P(E_1 \cap E_2) = P(E_1)P(E_2)$.
Therefore, for $A^c$ and $B^c$:

The calculated value 0.3 matches option B.