Solution

Let 

$I_i$ represent that house $i$ is insured against fire.

Given: $P(I_i)=0.6,~ \forall~ i \in \{1,2,3,4\}$

Finding probability distribution of $$xx:

$We\; use\; independence\; of\; purchase\; of$

$insurance\; for\; houses\; and\; multiplication\; rule$

$to\; calculate\; the\; the\; following\; probabilities.$

            

$$\begin{array}{rl}P(x\ge 3)& \\ & =P(x=3)+P(x=4)\\ & =0.3456+0.1296\\ & =0.4752\end{array}$$

Answer

P(X > 3) = 0.4752