Let $p(x)_{t}$ be the probability that a person aged $x$ survives until at least age $x+t$. Suppose we are given the following:
- $p(x)_{1} = 0.99$
- $p(x+1)_{1} = 0.985$
- $p(x+1)_{3} = 0.95$
- $q(x+3)_1 = 0.02$
Note that $q(x)_{t} = 1-p(x)_{t}$. What is $p(x+1)_{2}$?
So we want to find the probability that a person aged $x+1$ survives until at least age $x+3$. So $p(x+1)_{2} = p(x+1)_{1} \cdot p(x+2)_{1}$
But we don't know those values. That is, we don't know $ p(x+2)_{1}$.