2 more questions regarding Bayes Theorem

I don't understand why my answer is wrong. My understand of likelihood is the P ( Data | model). For example, if the model is that a coin is fair, and the coin was flipped 10 times and came up heads 6 times, then the likelihood is (some binomial distribution math goes here... unsure what it is actually... I think it's $6 choose 10 * 0.5 ^ 6 * 0.5 ^ 4$. Is that right?)

1. You go to Las Vegas and sit down at a slot machine. You are told by a highly reliable source that, for each spin, the probability of hitting the jackpot is either 1 in 1,000 or 1 in 1,000,000, but you have no prior information to tell you which of the two it is. You play ten times, but do not win the jackpot. What is the posterior probability that the true odds of hitting the jackpot are 1 in 1,000?

So is the math going to be:

$\frac{true-positive}{true-positive + false-positive}$

$\frac{(\frac{999}{1000}) ^{10} * \frac{1}{1000}}{(\frac{999}{1000}) ^{10} * \frac{1}{1000} + (\frac{999999}{1000000}) ^{10}}$