Two dice are thrown simultaneously. Given that sum of the numbers is NOT more than 5, what is the probability that sum is more than 3?

Question

amistre64 · Answer

how many ways can you get a sum of 3?

how many ways can you get a sum of 5 or less?

amistre64 · Answer

1,2  2,1 ... 2 cases

1,4  4,1   2,3  3,2   4 cases = 5
1,3 3,1 2,2             3 cases = 4
 ...                          2 cases = 3 per above
                              0 cases = 1

so 9 cases results in a 5 or less,  2 of which are 3

amistre64 · Answer

1 2 3 4 5 6
1  2 3 4 5  .  .
2  3 4 5  .  .  .
3  4 5  .  .  .  .
4  5  .  .  .  .  .
5
6

given that there are 9 cases,  i see 2 of them that fit the bill

amistre64 · Answer

or is that 10 cases ... these old eyes are growing dim :/

anonymous · Answer

o-o

amistre64 · Answer

$$P(A|B)=\frac{P(A\cap B)}{P(B)}$$
$$\frac{2/36}{10/36}=\frac2{10}$$