In life contingencies notation, tpx denotes the probability that a life aged x survives t years. Which statement best describes tpx?

• A. The probability that a life aged x survives at least t years
• B. The probability that a life aged x dies within t years
• C. The probability of surviving to age x+t unconditionally
• D. The force of mortality at age x+t

Answer: (A)

tpx is the probability that a life aged x will survive t years, conditional on being alive at age x. In other words, starting now at age x, the person is expected to still be alive after t years. This is a conditional survival probability, often written as tpx = P(T_x > t | T_x > 0), and in life-table terms it equals l_{x+t} / l_x, since l_x is the number alive at age x and l_{x+t} is the number alive at age x+t for the same cohort.

This describes surviving at least t years, not dying within t years, and not an unconditional probability to reach age x+t from birth. It also is not the force of mortality, which is a rate mu_{x+t}, an instantaneous quantity, not a probability.