Question

Two six-sided fair dice are rolled simultaneously. The probability that the sum of the two numbers rolled is greater than 3, given that the sum of the numbers is not greater than 5, is . The probability that one of the numbers is a 6 and the sum of the two numbers is an odd number is .

Answer 1

Two 6-sided fair dice can land in 36 ways.

A).  How many ways can they land where the sum of the two numbers rolled is greater than 3, given that the sum of the numbers is not greater than 5 ?

Well, that's just a complicated way of saying that they show either 4 or 5.
There are  7  ways that can happen:

1 ... 3
3 ... 1
1 ... 4
4 ... 1
2 ... 2
2 ... 3
3 ... 2

So the probability is      7/36  =  about  19.4% .


B).  How many ways can they land where one of the numbers is a 6 and the sum of the two numbers is an odd number ?

There are  6  ways that can happen:

6 ... 1
1 ... 6
6 ... 3
3 ... 6
6 ... 5
5 ... 6

So the probability is  6/36  =  1/6  =  16-2/3 % .