# Given l_0 = 1000000 and q_x = 0.0034 for all x calculate l_30 ? whats the intuition and how do we go about this?

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Am assuming it will be wrong to say probabilities that the person aged x dies in 10 and 20 years will be the same. Contingencies .

You are correct, saying $$q_{x}$$ is the same for all ages is saying that the probability of dying within the next year, regardless of your age, is the same.
Now, if $$l_0=1 000 000$$ then to find out how many people are alive at age $$30$$ we need to multiply $$l_0$$ by the probability of surviving $$30$$ years. Since $$q_x$$ is the same for all ages, $$1-q_x=p_x$$ is also the same for all ages.
Consider finding $$l_1$$: $$l_1=l_0 \times p_0$$.
Applying this to $$l_{30}$$, we get that $$l_{30}=l_0 \times p_0 \times p_1 \times ... \times p_{29}=l_0 \times \left(p_x\right)^{30}=l_0 \times \left(1-q_x\right)^{30}$$