The husband is 35, the wife is 28 years old. What is the probability that in 20 years:

a) both are still alive? b) the husband is no longer alive?

c) the wife is no longer alive? d) both are already dead?

e) the husband has died, but the wife is still alive? f) the husband is still alive, but the wife has died?

According to the appropriate mortality table, out of 1000 newborns:

the 28th year of life is reached by 675,

the 35th year of life is reached by 630,

the 48th year of life is reached by 540,

the 55th year of life is reached by 486,
According to the mortality table, the probability that the husband

$$
20 \text { years later is still alive } v_{1}=\frac{486}{630}=\frac{27}{35} \text {, }
$$

the wife is still alive 20 years later $v_{2}=\frac{540}{675}=\frac{4}{5}$.

In the following, since we are dealing with independent events, we can apply the multiplication rule. According to this, the probability that 20 years later
a) both are still alive
$v_{a}=v_{1} v_{2}=\frac{27}{35} \cdot \frac{4}{5}=\frac{108}{175} \approx 0.617$,
b) the husband has already died
$v_{b}=1-v_{1}=1-\frac{27}{35}=\frac{8}{35} \approx 0.229$,
c) the wife has already died
$v_{c}=1-v_{2}=1-\frac{4}{5}=\frac{1}{5}=0.200$,
d) both have already died
$v_{d}=\left(1-v_{1}\right)\left(1-v_{2}\right)=\frac{8}{35} \cdot \frac{1}{5}=\frac{8}{175} \approx 0.046$,
e) the husband has died, but the woman is still alive
$v_{e}=\left(1-v_{1}\right) v_{2}=\frac{8}{35} \cdot \frac{4}{5}=\frac{32}{175} \approx 0.183$,
f) the husband is still alive, but the woman has died
$v_{f}=v_{1}\left(1-v_{2}\right)=\frac{27}{35} \cdot \frac{1}{5}=\frac{27}{175} \approx 0.154$,

Notice that cases a), d), e), and f) are mutually exclusive and together cover all possible cases, and therefore $v_{a}+v_{d}+v_{e}+v_{f}=\frac{108}{175}+\frac{8}{175}+\frac{32}{175}+\frac{27}{175}=1$.

Tibor Katz (Hajdúnánás, Kőrösi Csoma g. II. o. t.)