My mom is 85 and I'm 58. 85 backwards is 58. What's the odds of that happening when both are still living?

Question

Need to know the odds when both are living

Answer 1

Hi Kenneth,

        This is an interesting question which I think I have an answer to"

 

Let x=one of the digits 1…..9

Let y=one of the digits 1…..9

 

Then 10y+x<100 one of the ages is less than 100 years "still living" you could make this the life expectancy 

and  10x+y>10 the other is greater than 10 the younger is at least 10

the other constraint is that 10y+x>y+10. The older age is greater than the younger duh!!

This describes the region where the feasible solutions lie. It is a triangular area bounded by the three lines:

y=10-x/10, y=10-10x and y=x.

There are 36  feasible integer solutions in this region I plotted it and counted them. I'm sure there is a much more elegant way to count them but I haven't seen it yet.

There are 81 different combinations of 9 integers so the probability of the reverse ages is 36/81=4/9 so the odds are 5 to 4 against.

Sounds reasonable to me. What do you think?

Jim