# Joint lives: Intuition for formulae

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Attached is the answers to DHW exercises 9.2. b) and c). I am struggling with understanding the intuition behind these formulae. Please help :(

Finally, the reason why the joint life probability for the lives aged 30 and aged 40 can be separated into two probabilities is that they are independent, and hence allows for the manipulation from $$_tP_{xy}$$ to $$_tP_{x}$$$$_tP_{y}$$, and further allows for the expression $$_tq_{40}*_tp_{30}$$.