45 pointsyou roll two standard number cubes. what is the probability that the sum is odd, given than one of the number cubes shows a 4?

6/11

Step-by-step explanation:

We are not told which number cube shows a 4; it can be the first one or the second one.

If the first number cube is a 4, this gives us the options of:

4 and 1; 4 and 2; 4 and 3; 4 and 4; 4 and 5; 4 and 6.

However if the second number cube is a 4, this gives us

1 and 4; 2 and 4; 3 and 4; 4 and 4; 5 and 4; 6 and 4.

We cannot count "4 and 4" twice; this leaves us with 11 total possibilities.

Out of these 11, only the sum of 4 and an odd number will be odd:

1 and 4; 3 and 4; 5 and 4; 4 and 1; 4 and 3; 4 and 5.

There are 6 ways to have an odd sum out of 11 total possibilities; this gives us a probability of 6/11.