Two six sided fair dice are rolled simultaneously the probability that the sum of the two numbers is greater than 3, given that the sum of the numbers is not greater than 5, is

Step-by-step explanation:

If we have two six sided fair dice, then the sample space is 36, that is, the total number of sums that can result form those dices.

Now, let's write in two collums those dices

Dice 1      Dice 2

    1             1

    2            2

    3            3

    4            4

    5            5

    6            6

Now, we need to find the total number of sums that are between 3 and 5.

There are 4 sums that result in 5:

There are 3 sums that result in 4:

There are 2 sums that result in 3:

So, in total, there are 9 sums that have a result between 3 and 5, taking 3 and 5 as part of the solutions.

Then, we find the probability by diving the number of successul events and the total number of outcomes

Therefore, there's a 25% of changes to obtain a pair of numbers which sum is 3, 4 or 5.