It is false. It can be proven with a counterexample. The counterexample may be a rhombus. Rhombus is a quadrilateral, is not a rectangle and its diagonal bisect each other.
10% chance of burning out 100-10= 90% chance of not burning out 90% = 0.9 3 lightbulbs 0.9^3 = 0.729 = 72.9% The probability that all 3 lightbulbs stay lit by the end of the month is 72.9%