Roll a pair of dice (a) What is the probability of rolling at least 9?
I draw the table and I came up with and answer of 5/18 from adding P(9)+P(10)+P(11)+P(12)
(b) if one die rolls a 4, What is the probability of rolling at least 9?
From the table I see that P(9|4) = 2/8, P(10|4) = 2/9, for 11 and 12 the probability is zero.
Hence my answer to (b) is the sum of the two above probabilities which equals 17/36.
Are any of this answers correct or wrong?
Thanks for any help.
 A: I am not sure why you have $P(9|4)=\frac29$ but $P(10|4)=\frac2{8}$.   I think they have to be the same, perhaps $\frac16$, $\frac2{11}$ or $\frac2{10}$.
Since RowanS disagree with me on the second question, here is my table of each die and their sum, with each pairing equally probable.
    Red 1   2   3   4   5   6
Blue                            
1       2   3   4   5   6   7
2       3   4   5   6   7   8
3       4   5   6   7   8   9
4       5   6   7   8   9   10
5       6   7   8   9   10  11
6       7   8   9   10  11  12



*

*if the red die rolls a $4$, the probability of the sum being  at least $9$ is (looking at the column) $\dfrac{2}{6}=\dfrac13$

*if either die rolls a $4$, the probability of the sum being  at least $9$ is (looking at the column and row) $\dfrac{4}{11}$

*if exactly one rolls a $4$, the probability of the sum being  at least $9$ is (looking at the column and row but not where they intersect) $\dfrac{4}{10}=\dfrac25$
A: Answer for both the parts are given as below

