A probability math question?

I can't see this too clearly but I think all of them but 6 say 1/9, right? And 6 is 1/2? I'll proceed under those assumptions. Now for part 1, we know that the probability has to add up to 1 (I'm sure you'll get something if you roll), so we say that 1/2+1/9+1/9+1/9+1/9+k=1. Now, that's just 4/9+1/2=9/18+8/18=17/18, so k=1/18.

For part 2 we just have to find the probability in each scenario. If she picked the fair dice, the probability should be 1/3, whereas if she picked the biased dice it should be 11/18. Assuming she has an equal probability of picking either dice, we should just take the average and we find that 6/18+11/18=17/18, divide by 2 and our probability should be 17/36.

TECHNICALLY, the fact that she rolled a point doesn't ACTUALLY tell us anything about which dice she picked. The probability of her having picked a dice is still 50-50. However, I get what the problem is asking. It's saying, the probability of her getting a point with the fair dice is 1/3. However, the probability of having rolled the biased dice and getting a point is 11/18. Now, the likeliness of her having chosen a die is proportional to the likelihood of her getting a point with the die (since we know she did get that point), so the ratio is 11/18 to 1/3. That is, the answer should be 11/18, I believe.