Step 1 :A number cube labeled with numbers 1,2,3,4,5, and 6 is tossed. We are asked to find the odds in favor of the cube showing a number less than 3.
Step 2 :The odds in favor of an event are defined as the ratio of the number of successful outcomes to the number of unsuccessful outcomes.
Step 3 :In this case, the successful outcomes are the cube showing a number less than 3, which are 1 and 2. So there are 2 successful outcomes.
Step 4 :The unsuccessful outcomes are the cube showing a number equal to or greater than 3, which are 3, 4, 5, and 6. So there are 4 unsuccessful outcomes.
Step 5 :Therefore, the odds in favor of the cube showing a number less than 3 are 2 to 4, or simplified, 1 to 2.
Step 6 :Final Answer: \(\boxed{1: 2}\)