oh damn..I did a crucial mistake to consider that all digits must be odd

got to 1/20

(

only after I clicked the answer..I re-read the question and understood where I made the error

we have 10 digits, last one must be odd, thus 5 possible ways. first one has to be any digit except for 0 and last one, thus we have 8 ways to pick first digit. then second, we can pick from 8 ways (first one is picked, and last one too, but we did not consider 0 in the first two cases, hence we have here 8 ways), then 7 for the third digit, and 6 for the fourth.

we have 8*8*7*6*5

for a number to have 1 as first digit, and 9 as the last, no repeating digits: we have 1*8*7*6*1

THEN, the probability is

8*7*6/8*8*7*6*5 = 1/40...