Final answer:
The probability that the blue die is less than 7 and the green die is 4 is 1/6, since the blue die always meets its condition and the green die has a 1 in 6 chance of being 4.
Step-by-step explanation:
The question relates to the subject of probability, specifically concerning the outcome of rolling two dice of different colors. To find the probability that the blue die is less than 7 and the green die is 4, we must consider the possible outcomes of each die separately. A six-sided die, which is typical, has the numbers 1 through 6, so any roll of a blue die will naturally be less than 7. Therefore, the blue die's condition is always met.
The green die must show a 4 for the requirement to be met. Since a six-sided die has only one face with the number 4, we have a 1 in 6 chance of rolling a 4 for the green die. Because the blue die always meets the condition of being less than 7 (there are six possible outcomes for the blue die), and the green die has a 1 in 6 chance of being a 4, we can calculate the joint probability:
Probability that the blue is less than 7 and the green is 4 = Chance of blue die being less than 7 × Chance of green die being 4.
Since the chance of the blue die meeting its condition is 1 (it always will), and the chance of the green die being a 4 is 1/6, we get:
Probability = 1 × 1/6 = 1/6.
The correct answer choice is a) 1/6.