19. You roll two standard number cubes. What is the probability that the sum is odd, given than one of the number cubes shows a 1? Show your work.

there are 6 numbers per cube,

the chance of rolling one and getting the number 1 is a 1/6 probability

for the sum to be odd, you need to roll either a 2, 4 or 6 on the second cube so that gives you a 3/6 probability

so 1/6 x 3/6 = 3/36 which can be reduced to 1/12

so you have a 1/12 probability