### Instruction: Two 6-sided dice, one red and one green, are rolled.  What is the probability that the red die shows an odd number and the green die shows a number that is a perfect square?### Response: I need to find the fraction of outcomes that satisfy both conditions: red is odd and green is a perfect square.
To do that, I can multiply the probabilities of each condition separately, since they are independent events.
The probability that the red die shows an odd number is 1/2, since there are three odd numbers (1, 3, and 5) out of six possible outcomes.
The probability that the green die shows a perfect square is 1/3, since there are two perfect squares (1 and 4) out of six possible outcomes.
Multiplying 1/2 and 1/3, I get 1/6, which is the probability of the desired event.