First of all, I have obtained using the binomial distribution that the probability of obtaining twice or more heads than tails is $0.0577$ (value which corresponds with the solution of the textbook). However, I am having problems with the conditional probability of the title.
I know that the possible number of heads that verify the condition are $14,15,16,17,18,19$ or $20$, and only three of them are odd. So, I thought of $3/20$ but the solution must be $0.2754$. Any help? Thanks.