Given; (odds against A) = 5:4, Find P(A).

Question

Given; (odds against A) = 5:4, Find P(A).

would the answer be 5/9?

I did P(A) = h/k+h, odds in favour = 5 (h):4 (k) -> P(A) = 5/4+5 = 5/9, but it said the answer is 4/9 and I don't understand why because I was given a similar question to this which is, Given odds against A = 1:5, determine P(A) and did the same thing, P(A) = h/k+h, odds in favour = 1 (h):5(k) -> P(A) = 1/5+1 = 1/6 which I believe is correct.

What did I do wrong exactly? Can someone please explain, thank you so much if you can!

Answer 1

odds against A a:b, p(A) = b/(a+b)

Think logically. if adds against are 5 : 4, that means that more likely that A doesnt happen than happens (as 5 > 4) so p(A) must be less than 1/2.

5/9 > 1/2 so p(A) cant be 5/9