Final answer:
The probability that a red die and a blue die will show different numbers when rolled together is 5/6. This is because there are 36 possible outcomes, 6 of which have the same number on both dice. Subtracting the probability of the same numbers from the total probability gives us the probability of different numbers.
Step-by-step explanation:
The question deals with finding the probability that a red die and a blue die, when thrown, will show different numbers. As each die has 6 faces, there are a total of 36 possible outcomes when both dice are rolled (6 outcomes from the red die multiplied by 6 outcomes from the blue die). To find the probability that the numbers are the same, we would look for outcomes where both dice have the same number (i.e., (1,1), (2,2), ..., (6,6)), which makes for 6 such outcomes.
The probability they are the same is therefore 6 out of 36, which can be simplified to 1/6. To find the probability that they are different, we subtract this probability from 1 (the total probability for all outcomes) because the events 'numbers are the same' and 'numbers are different' are complementary.
So, the probability that the two dice show different numbers is 1 - 1/6, which simplifies to 5/6.