The odds against her husband living till he is 85 are 7 : 5. 

Let P(H’) = P(husband dies before he is 85) = 7/7+5 = 7/12

So, the probability that the husband would be alive till age 85 

P(H) = 1 – P(H’) = 1 – 7/12 = 5/12

Similarly, P(W’) = P(Wife dies before she is 81) 

Since the odds against wife will be alive till she is 81 are 5 : 3.

∴ P(W’) = 5/5+3 = 5/8

So, the probability that the wife would be alive till age 81 

P(W) = 1 – P(W’) = 1 – 5/8 = 3/8

(i) Required probability 

P(H ∪ W) = P(H) + P(W) – P(H ∩ W) 

Since H and W are independent events, P(H ∩ W) = P(H) . P(W) 

∴ Required probability = P(H) + P(W) – P(H) . P(W)

= \(\frac {5}{12} + \frac {3}{8} -\frac{5}{12}\times\frac{3}{8}\)

= 40+36-15/96

= 61/96

(ii) Required probability = P(H ∩ W’) + P(H’ ∩ W) 

Since H and W are independent events, H’ and W’ are also independent events. 

∴ Required probability = P(H) . P(W’) + P(H’) . P(W)

= \(\frac {5}{12} + \frac {5}{8}+\frac{7}{12}\times\frac{3}{8}\)

= 25+21/96

46/96

= 23/48