The probability that a blue number cube will show a number less than 7 is 6/6, or 1. The probability that a green number cube will show a number less than 3 is 2/6, or 1/3. To find the probability that both events will occur, we multiply the probabilities together:
P(blue less than 7 and green less than 3) = 1 * (1/3) = 1/3
Therefore, the probability that a blue number cube will show a number less than 7 and a green number cube will show a number less than 3 is 1/3.