calculate the probability that a person aged 17 will die at age 19.(Contingencies)

+1 vote
62 views

Given that $$l_{19} = 100000$$ and that $$q_x=0.000034x^2$$. calculate $$l_{17}$$.

I tried to use $$_{2}p_{17}$$ but i got stuck where i had to compute $$\frac{l_{19}}{(1-_2q_{17})}$$ because i already had a value of $$q_{17}$$ not $$_2q_{17}$$. it would be wrong for me to multiply $$q_{17}$$ by 2 right?

It would indeed be wrong to multiply $$q_{17}$$ by $$2$$. Also remember that $$_{2}{q}_{17} \neq _{1}{q}_{17} \times _{1}{q}_{18}$$. Death probabilities don't work like this 'cause once you're dead, you're dead - you can't find the probability of dying at age 18 if you already died at 17!
However, you absolutely can do that with survival probabilities! So, to calculate $$l_{17}$$ we need to change the death probabilities into survival probabilities and then work with those: $$_2p_{17}=p_{17} \times p_{18}=(1-q_{17}) \times (1-q_{18})$$