Q.A fair die is thrown two times. Find the probability that a) sum of the numbers on them is 5 b) sum of the numbers on them is at least 8 c) first throw gives a multiple of 2 and second throw gives a multiple of 3 d) product of numbers on them is 12.

$n(S)=36$ throughout.

a) Sum $=5$: $(1,4),(2,3),(3,2),(4,1)$, 4 outcomes, $P=4/36=1/9$.

b) Sum $\ge8$: sums 8,9,10,11,12 give 5+4+3+2+1=15 outcomes, $P=15/36=5/12$.

c) First throw a multiple of 2 (2,4,6: 3 choices), second throw a multiple of 3 (3,6: 2 choices): $3\times2=6$ outcomes, $P=6/36=1/6$. …

List/count the favourable outcome pairs on the 36-outcome two-dice sample space for ea …

In (b), forgetting to include sum=12, or in (d), missing the pair (3,4 …