GRE Exam Numerical Ability Probability

A and B take turn in throwing 2 dice ; the 1st to throw 9 being awarded. what is the ratio of probabilities of their winning if A has the first throw?

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V can apply Bayes theorem here..
Probability of A getting selected is 1/2 and so as B which is also 1/2..
Sample space=36(6^2)
We get 9 if the in the first throw we get (4,5) & (5,4)
Probability of getting 9 is therefore (2/36)..
Now using bayes theorem we get ((1/2)*(2/36))/((1/2)(2/36)+(1/2)(2/36)) which we get as 1/2 so the ratio is 1:2..
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GRE Other Question

a number is a palindrome if it reads the same from left to right n vice versa. E.g: 24742. What is the probability that a 3 digit number chosen at random is a palindrome? two numbers are selected at random from the integers 1 through 9 the sum is even. what is the probability of both are odd?