probability odds question

[Arushi :))]

The odds are 9 to 5 against a person who is 50 years living till he is 70 and 8 to 6 against a person who is 60 living till he is 80.
Find the probability that at least one of them will be alive after 20 years.

[jack]

let us define the events:
E1: A will be alive till 70
E2: B will be alive till 80
P(E1)=5/14  ,P(E2)=6/14

E1 and E2 are independent
therefore: p(E1^E2)
5/14*6/14=30/196

so P(at least one of them will be alive)=5/14+6/14-30/196
31/49

[The Villain]

you can also do as
Let A be prob 1st person will live 70 yrs
Let B be prob 2nd person will live 80 yrs
P(A)=5/14 ...thefore P(A not)=9/14
P(B)=6/14.....therfore P(B not)=8/14
P(atleast one of them will be alive)= 1- P(none will be alive)
                           =1-9/14*8/14
                            =31/49