probability question

Question

Find the probability of rolling a sum of a five first and then a sum of a ten when a pair of dice is rolled twice.

Answer 1

n(s) sample space= when dice rolled two times

n(s) =6^2

36

then get the sum of the first 5 after rolling a dice (1,4), (2,3), (3,2),(4,1) if I go (1,1), (1,2),(1,3),(1,4), (1,5), (1,6)..........so on 6 times

So I got 4 possible outcome that gives the sum 5

that will be P(5)= 4/36

like that, I get 3 possible outcome that gives the sum of 10 these are (4,6) (5,5), (6,4)

so P(10)= 3/36

P(5)*p(10)=4/36 *3/36

1/9*1/12

= 1/108

Answer 2