Final answer:
The probability of rolling a pair of fours on the next roll of two six-sided dice is 1/36, since each roll is independent and the result of one does not affect the outcome of the other.
Step-by-step explanation:
The probability that Jim will roll a pair of fours on the next roll of two six-sided dice is a question of simple probability, not influenced by his previous rolls, since each roll is an independent event. The question is asking, "If Jim rolls a pair of six-sided dice, what is the probability that he will roll a pair of fours?" To calculate this, we consider each die separately and then use the product rule to combine the probabilities.
There is one way to roll a four on a single six-sided die, and there are six possible outcomes when the die is rolled. Thus, the probability of rolling a four on a single die is 1/6. As both dice are fair and independent, the probability of rolling a pair of fours is the product of the individual probabilities:
Probability of pair of fours = (1/6) x (1/6) = 1/36
Therefore, the correct answer is A) 1/36.