Under H

0, a random variable has the cumulative distribution function ; and under H1, it has the cumulative distribution function
Question: If the two hypotheses have equal prior probability, for what values of x is the posterior probability of H

0 greater than that of H

1?
This is what I did:

Since I know that

, Given that the prior probability is equal will yield

However,

given that 0<x<1, so it seems that for all values the statement is true, but the answer is apparent not as above.

Hope someone can help me. Thanks