Final answer:
The probability that the product of the numbers on three ordinary dice is less than 216 is 1/2, calculated by considering the 5 suitable outcomes for each die to avoid products of 216 or greater. the correct answer is (d).
Step-by-step explanation:
The student has asked, "What is the probability that the product of the numbers rolled on three ordinary dice is less than 216?"
To answer this, we need to find the total number of possible outcomes for three dice rolls and then determine how many of those outcomes result in a product less than 216.
There are 6 possible outcomes per die, so with three dice, there are 6 x 6 x 6 = 216 total possible outcomes. Now to consider the condition, each number that comes up in the roll of a die is independent of others and can be any number from 1 to 6. We know that if any die shows a 6, the product must be at least 216, which is not what we want. Thus, we avoid rolling a 6. So, for each die, we have 5 suitable outcomes, and the acceptable combinations would be 5 x 5 x 5 = 125.
To determine the probability, we use this formula: Probability = Number of favorable outcomes / Total number of possible outcomes, which in this case is 125/216. This fraction simplifies to roughly 0.5787, which is closest to 1/2
Therefore, the correct answer to the student's question is (d) 1/2.